Number - Fractional Indices Questions
Question 1
Evaluate:
a) $9^{\frac12}$
a
$3$
Question ID: 10350010010
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b) $8^{\frac13}$
a
$2$
Question ID: 10350010020
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c) $81^{\frac14}$
a
$3$
Question ID: 10350010030
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d) $16^{\frac12}$
a
$4$
Question ID: 10350010040
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e) $32^{\frac15}$
a
$2$
Question ID: 10350010050
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f) $1000^{\frac13}$
a
$10$
Question ID: 10350010060
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g) $64^{\frac16}$
a
$2$
Question ID: 10350010070
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h) $1^{\frac15}$
a
$1$
Question ID: 10350010080
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Question 2
Evaluate:
a) $\left(\frac{1}{100}\right)^{\frac12}$
a
$\frac{1}{10}$
Question ID: 10350020010
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b) $\left(\frac{1}{8}\right)^{\frac13}$
a
$\frac12$
Question ID: 10350020020
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c) $\left(\frac{1}{81}\right)^{\frac14}$
a
$\frac13$
Question ID: 10350020030
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d) $\left(\frac{1}{125}\right)^{\frac13}$
a
$\frac15$
Question ID: 10350020040
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e) $\left(\frac{1}{49}\right)^{\frac12}$
a
$\frac17$
Question ID: 10350020050
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f) $\left(\frac{1}{256}\right)^{\frac14}$
a
$\frac14$
Question ID: 10350020060
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Question 3
Evaluate:
a) $\left(\frac{9}{16}\right)^{\frac12}$
a
$\frac34$
Question ID: 10350030010
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b) $\left(\frac{8}{27}\right)^{\frac13}$
a
$\frac23$
Question ID: 10350030020
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c) $\left(\frac{16}{81}\right)^{\frac14}$
a
$\frac23$
Question ID: 10350030030
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d) $\left(\frac{16}{81}\right)^{\frac12}$
a
$\frac49$
Question ID: 10350030040
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e) $\left(\frac{27}{125}\right)^{\frac13}$
a
$\frac35$
Question ID: 10350030050
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f) $\left(\frac{81}{4}\right)^{\frac12}$
a
$\frac92$
Question ID: 10350030060
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g) $\left(\frac{1000}{27}\right)^{\frac13}$
a
$\frac{10}{3}$
Question ID: 10350030070
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h) $\left(\frac{121}{16}\right)^{\frac12}$
a
$\frac{11}{4}$
Question ID: 10350030080
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Question 4
Evaluate:
a) $9^{\frac32}$
a
$27$
Question ID: 10350040010
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b) $16^{\frac32}$
a
$64$
Question ID: 10350040020
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c) $4^{\frac52}$
a
$32$
Question ID: 10350040030
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d) $27^{\frac23}$
a
$9$
Question ID: 10350040040
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e) $16^{\frac34}$
a
$8$
Question ID: 10350040050
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f) $1000^{\frac53}$
a
$100000$
Question ID: 10350040060
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g) $32^{\frac65}$
a
$64$
Question ID: 10350040070
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h) $125^{\frac43}$
a
$625$
Question ID: 10350040080
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Question 5
Evaluate, leaving your answers as surds where necessary.
a) $2^{\frac12}$
a
$\sqrt2$
Question ID: 10350050010
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b) $10^{\frac12}$
a
$\sqrt{10}$
Question ID: 10350050020
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c) $5^{\frac13}$
a
$\sqrt[3]5$
Question ID: 10350050030
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d) $7^{\frac14}$
a
$\sqrt[4]7$
Question ID: 10350050040
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e) $\left(\frac35\right)^{\frac12}$
a
$\frac{\sqrt3}{\sqrt5}$
Question ID: 10350050050
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f) $\left(\frac17\right)^{\frac12}$
a
$\frac{1}{\sqrt7}$
Question ID: 10350050060
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g) $\left(\frac45\right)^{\frac12}$
a
$\frac{2}{\sqrt5}$
Question ID: 10350050070
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h) $\left(\frac79\right)^{\frac12}$
a
$\frac{\sqrt3}{3}$
Question ID: 10350050080
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i) $\left(\frac83\right)^{\frac13}$
a
$\frac{2}{\sqrt[3]3}$
Question ID: 10350050090
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j) $\left(\frac{81}{9}\right)^{\frac14}$
a
$\frac{4}{\sqrt3}$
Question ID: 10350050100
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Question 6
Evaluate, leaving your answers as surds where necessary.
a) $2^{\frac32}$
a
$2\sqrt2$
Question ID: 10350060010
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b) $3^{\frac32}$
a
$3\sqrt3$
Question ID: 10350060020
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c) $5^{\frac52}$
a
$25\sqrt5$
Question ID: 10350060030
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d) $7^{\frac43}$
a
$7\sqrt[3]7$
Question ID: 10350060040
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e) $11^{\frac73}$
a
$121\sqrt[3]{11}$
Question ID: 10350060050
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f) $1^{\frac54}$
a
$1$
Question ID: 10350060060
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Question 7
Evaluate, leaving your answers as surds where necessary.
a) $5^{\frac23}$
a
$\sqrt[3]{25}$ or $\left(\sqrt[3]5\right)^2$
Question ID: 10350070010
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b) $13^{\frac23}$
a
$\sqrt[3]{169}$ or $\left(\sqrt[3]{13}\right)^2$
Question ID: 10350070020
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c) $3^{\frac45}$
a
$\sqrt[5]{81}$ or $\left(\sqrt[5]{3}\right)^4$
Question ID: 10350070030
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d) $21^{\frac74}$
a
$\sqrt[4]{{21}^7}$ or $\left(\sqrt[4]{21}\right)^7$
Question ID: 10350070040
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e) $9^{\frac23}$
a
$\sqrt[3]{81}$ or $\left(\sqrt[3]{9}\right)^2$
Question ID: 10350070050
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f) $4^{\frac43}$
a
$\sqrt[3]{256}$ or $\left(\sqrt[3]{4}\right)^4$
Question ID: 10350070060
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g) $16^{\frac75}$
a
$\sqrt[5]{16^7}$ or $\left(\sqrt[5]{16}\right)^7$
Question ID: 10350070070
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h) $\left(\frac35\right)^{\frac37}$
a
$\sqrt[7]{\frac{27}{125}}$ or $\left(\sqrt[7]{\left(\frac35\right)}\right)^3$
Question ID: 10350070080
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Question 8
Evaluate, leaving your answers as simplified surds where necessary.
a) $8^{\frac32}$
a
$16\sqrt2$
Question ID: 10350080010
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b) $12^{\frac32}$
a
$24\sqrt3$
Question ID: 10350080020
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c) $20^{\frac32}$
a
$40\sqrt5$
Question ID: 10350080030
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d) $8^{\frac52}$
a
$128\sqrt2$
Question ID: 10350080040
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e) $16^{\frac53}$
a
$16\sqrt[3]{256}$
Question ID: 10350080050
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f) $162^{\frac74}$
a
$4374\sqrt[4]{8}$
Question ID: 10350080060
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Question 9
Evaluate:
a) $\left(\frac{9}{16}\right)^{\frac{1}{3}}\times\left(\frac{9}{16}\right)^{\frac{1}{6}}$
a
$\frac34$
Question ID: 10350090010
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b) $\left(\frac{1000}{27}\right)^{\frac{1}{5}}\times\left(\frac{1000}{27}\right)^{\frac{2}{15}}$
a
$\frac{10}{3}$
Question ID: 10350090020
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c) $\left(5\frac{1}{16}\right)^{\frac{7}{10}}\times\left(5\frac{1}{16}\right)^{\frac{1}{20}}$
a
$\frac{27}{8}$ or $3\frac38$
Question ID: 10350090030
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d) $\left(\frac{1}{3125}\right)^{\frac{1}{2}}\div\left(\frac{1}{3125}\right)^{0.1}$
a
$\frac{1}{25}$
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e) $\left(\left(\frac{343}{125}\right)^{\frac{1}{9}}\right)^6$
a
$\frac{49}{25}$
Question ID: 10350090050
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f) $\sqrt{\frac{\left(0.\dot4\right)^{31}}{\left(\frac{16}{81}\right)^{13}}}$
a
$\frac{32}{243}$
Question ID: 10350090060
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Question 1
Evaluate:
a) $9^{\frac12}$
b) $8^{\frac13}$
c) $81^{\frac14}$
d) $16^{\frac12}$
e) $32^{\frac15}$
f) $1000^{\frac13}$
g) $64^{\frac16}$
h) $1^{\frac15}$
Question 2
Evaluate:
a) $\left(\frac{1}{100}\right)^{\frac12}$
b) $\left(\frac{1}{8}\right)^{\frac13}$
c) $\left(\frac{1}{81}\right)^{\frac14}$
d) $\left(\frac{1}{125}\right)^{\frac13}$
e) $\left(\frac{1}{49}\right)^{\frac12}$
f) $\left(\frac{1}{256}\right)^{\frac14}$
Question 3
Evaluate:
a) $\left(\frac{9}{16}\right)^{\frac12}$
b) $\left(\frac{8}{27}\right)^{\frac13}$
c) $\left(\frac{16}{81}\right)^{\frac14}$
d) $\left(\frac{16}{81}\right)^{\frac12}$
e) $\left(\frac{27}{125}\right)^{\frac13}$
f) $\left(\frac{81}{4}\right)^{\frac12}$
g) $\left(\frac{1000}{27}\right)^{\frac13}$
h) $\left(\frac{121}{16}\right)^{\frac12}$
Question 4
Evaluate:
a) $9^{\frac32}$
b) $16^{\frac32}$
c) $4^{\frac52}$
d) $27^{\frac23}$
e) $16^{\frac34}$
f) $1000^{\frac53}$
g) $32^{\frac65}$
h) $125^{\frac43}$
Question 5
Evaluate, leaving your answers as surds where necessary.
a) $2^{\frac12}$
b) $10^{\frac12}$
c) $5^{\frac13}$
d) $7^{\frac14}$
e) $\left(\frac35\right)^{\frac12}$
f) $\left(\frac17\right)^{\frac12}$
g) $\left(\frac45\right)^{\frac12}$
h) $\left(\frac79\right)^{\frac12}$
i) $\left(\frac83\right)^{\frac13}$
j) $\left(\frac{81}{9}\right)^{\frac14}$
Question 6
Evaluate, leaving your answers as surds where necessary.
a) $2^{\frac32}$
b) $3^{\frac32}$
c) $5^{\frac52}$
d) $7^{\frac43}$
e) $11^{\frac73}$
f) $1^{\frac54}$
Question 7
Evaluate, leaving your answers as surds where necessary.
a) $5^{\frac23}$
b) $13^{\frac23}$
c) $3^{\frac45}$
d) $21^{\frac74}$
e) $9^{\frac23}$
f) $4^{\frac43}$
g) $16^{\frac75}$
h) $\left(\frac35\right)^{\frac37}$
Question 8
Evaluate, leaving your answers as simplified surds where necessary.
a) $8^{\frac32}$
b) $12^{\frac32}$
c) $20^{\frac32}$
d) $8^{\frac52}$
e) $16^{\frac53}$
f) $162^{\frac74}$
Question 9
Evaluate:
a) $\left(\frac{9}{16}\right)^{\frac{1}{3}}\times\left(\frac{9}{16}\right)^{\frac{1}{6}}$
b) $\left(\frac{1000}{27}\right)^{\frac{1}{5}}\times\left(\frac{1000}{27}\right)^{\frac{2}{15}}$
c) $\left(5\frac{1}{16}\right)^{\frac{7}{10}}\times\left(5\frac{1}{16}\right)^{\frac{1}{20}}$
d) $\left(\frac{1}{3125}\right)^{\frac{1}{2}}\div\left(\frac{1}{3125}\right)^{0.1}$
e) $\left(\left(\frac{343}{125}\right)^{\frac{1}{9}}\right)^6$
f) $\sqrt{\frac{\left(0.\dot4\right)^{31}}{\left(\frac{16}{81}\right)^{13}}}$
Answers
Question 1
a) $3$
b) $2$
c) $3$
d) $4$
e) $2$
f) $10$
g) $2$
h) $1$
Question 2
a) $\frac{1}{10}$
b) $\frac12$
c) $\frac13$
d) $\frac15$
e) $\frac17$
f) $\frac14$
Question 3
a) $\frac34$
b) $\frac23$
c) $\frac23$
d) $\frac49$
e) $\frac35$
f) $\frac92$
g) $\frac{10}{3}$
h) $\frac{11}{4}$
Question 4
a) $27$
b) $64$
c) $32$
d) $9$
e) $8$
f) $100000$
g) $64$
h) $625$
Question 5
a) $\sqrt2$
b) $\sqrt{10}$
c) $\sqrt[3]5$
d) $\sqrt[4]7$
e) $\frac{\sqrt3}{\sqrt5}$
f) $\frac{1}{\sqrt7}$
g) $\frac{2}{\sqrt5}$
h) $\frac{\sqrt3}{3}$
i) $\frac{2}{\sqrt[3]3}$
j) $\frac{4}{\sqrt3}$
Question 6
a) $2\sqrt2$
b) $3\sqrt3$
c) $25\sqrt5$
d) $7\sqrt[3]7$
e) $121\sqrt[3]{11}$
f) $1$
Question 7
a) $\sqrt[3]{25}$ or $\left(\sqrt[3]5\right)^2$
b) $\sqrt[3]{169}$ or $\left(\sqrt[3]{13}\right)^2$
c) $\sqrt[5]{81}$ or $\left(\sqrt[5]{3}\right)^4$
d) $\sqrt[4]{{21}^7}$ or $\left(\sqrt[4]{21}\right)^7$
e) $\sqrt[3]{81}$ or $\left(\sqrt[3]{9}\right)^2$
f) $\sqrt[3]{256}$ or $\left(\sqrt[3]{4}\right)^4$
g) $\sqrt[5]{16^7}$ or $\left(\sqrt[5]{16}\right)^7$
h) $\sqrt[7]{\frac{27}{125}}$ or $\left(\sqrt[7]{\left(\frac35\right)}\right)^3$
Question 8
a) $16\sqrt2$
b) $24\sqrt3$
c) $40\sqrt5$
d) $128\sqrt2$
e) $16\sqrt[3]{256}$
f) $4374\sqrt[4]{8}$
Question 9
a) $\frac34$
b) $\frac{10}{3}$
c) $\frac{27}{8}$ or $3\frac38$
d) $\frac{1}{25}$
e) $\frac{49}{25}$
f) $\frac{32}{243}$
Question 1
Evaluate:
a) $9^{\frac12}$
b) $8^{\frac13}$
c) $81^{\frac14}$
d) $16^{\frac12}$
e) $32^{\frac15}$
f) $1000^{\frac13}$
g) $64^{\frac16}$
h) $1^{\frac15}$
Question 2
Evaluate:
a) $\left(\frac{1}{100}\right)^{\frac12}$
b) $\left(\frac{1}{8}\right)^{\frac13}$
c) $\left(\frac{1}{81}\right)^{\frac14}$
d) $\left(\frac{1}{125}\right)^{\frac13}$
e) $\left(\frac{1}{49}\right)^{\frac12}$
f) $\left(\frac{1}{256}\right)^{\frac14}$
Question 3
Evaluate:
a) $\left(\frac{9}{16}\right)^{\frac12}$
b) $\left(\frac{8}{27}\right)^{\frac13}$
c) $\left(\frac{16}{81}\right)^{\frac14}$
d) $\left(\frac{16}{81}\right)^{\frac12}$
e) $\left(\frac{27}{125}\right)^{\frac13}$
f) $\left(\frac{81}{4}\right)^{\frac12}$
g) $\left(\frac{1000}{27}\right)^{\frac13}$
h) $\left(\frac{121}{16}\right)^{\frac12}$
Question 4
Evaluate:
a) $9^{\frac32}$
b) $16^{\frac32}$
c) $4^{\frac52}$
d) $27^{\frac23}$
e) $16^{\frac34}$
f) $1000^{\frac53}$
g) $32^{\frac65}$
h) $125^{\frac43}$
Question 5
Evaluate, leaving your answers as surds where necessary.
a) $2^{\frac12}$
b) $10^{\frac12}$
c) $5^{\frac13}$
d) $7^{\frac14}$
e) $\left(\frac35\right)^{\frac12}$
f) $\left(\frac17\right)^{\frac12}$
g) $\left(\frac45\right)^{\frac12}$
h) $\left(\frac79\right)^{\frac12}$
i) $\left(\frac83\right)^{\frac13}$
j) $\left(\frac{81}{9}\right)^{\frac14}$
Question 6
Evaluate, leaving your answers as surds where necessary.
a) $2^{\frac32}$
b) $3^{\frac32}$
c) $5^{\frac52}$
d) $7^{\frac43}$
e) $11^{\frac73}$
f) $1^{\frac54}$
Question 7
Evaluate, leaving your answers as surds where necessary.
a) $5^{\frac23}$
b) $13^{\frac23}$
c) $3^{\frac45}$
d) $21^{\frac74}$
e) $9^{\frac23}$
f) $4^{\frac43}$
g) $16^{\frac75}$
h) $\left(\frac35\right)^{\frac37}$
Question 8
Evaluate, leaving your answers as simplified surds where necessary.
a) $8^{\frac32}$
b) $12^{\frac32}$
c) $20^{\frac32}$
d) $8^{\frac52}$
e) $16^{\frac53}$
f) $162^{\frac74}$
Question 9
Evaluate:
a) $\left(\frac{9}{16}\right)^{\frac{1}{3}}\times\left(\frac{9}{16}\right)^{\frac{1}{6}}$
b) $\left(\frac{1000}{27}\right)^{\frac{1}{5}}\times\left(\frac{1000}{27}\right)^{\frac{2}{15}}$
c) $\left(5\frac{1}{16}\right)^{\frac{7}{10}}\times\left(5\frac{1}{16}\right)^{\frac{1}{20}}$
d) $\left(\frac{1}{3125}\right)^{\frac{1}{2}}\div\left(\frac{1}{3125}\right)^{0.1}$
e) $\left(\left(\frac{343}{125}\right)^{\frac{1}{9}}\right)^6$
f) $\sqrt{\frac{\left(0.\dot4\right)^{31}}{\left(\frac{16}{81}\right)^{13}}}$
Answers
Question 1
a) $3$
b) $2$
c) $3$
d) $4$
e) $2$
f) $10$
g) $2$
h) $1$
Question 2
a) $\frac{1}{10}$
b) $\frac12$
c) $\frac13$
d) $\frac15$
e) $\frac17$
f) $\frac14$
Question 3
a) $\frac34$
b) $\frac23$
c) $\frac23$
d) $\frac49$
e) $\frac35$
f) $\frac92$
g) $\frac{10}{3}$
h) $\frac{11}{4}$
Question 4
a) $27$
b) $64$
c) $32$
d) $9$
e) $8$
f) $100000$
g) $64$
h) $625$
Question 5
a) $\sqrt2$
b) $\sqrt{10}$
c) $\sqrt[3]5$
d) $\sqrt[4]7$
e) $\frac{\sqrt3}{\sqrt5}$
f) $\frac{1}{\sqrt7}$
g) $\frac{2}{\sqrt5}$
h) $\frac{\sqrt3}{3}$
i) $\frac{2}{\sqrt[3]3}$
j) $\frac{4}{\sqrt3}$
Question 6
a) $2\sqrt2$
b) $3\sqrt3$
c) $25\sqrt5$
d) $7\sqrt[3]7$
e) $121\sqrt[3]{11}$
f) $1$
Question 7
a) $\sqrt[3]{25}$ or $\left(\sqrt[3]5\right)^2$
b) $\sqrt[3]{169}$ or $\left(\sqrt[3]{13}\right)^2$
c) $\sqrt[5]{81}$ or $\left(\sqrt[5]{3}\right)^4$
d) $\sqrt[4]{{21}^7}$ or $\left(\sqrt[4]{21}\right)^7$
e) $\sqrt[3]{81}$ or $\left(\sqrt[3]{9}\right)^2$
f) $\sqrt[3]{256}$ or $\left(\sqrt[3]{4}\right)^4$
g) $\sqrt[5]{16^7}$ or $\left(\sqrt[5]{16}\right)^7$
h) $\sqrt[7]{\frac{27}{125}}$ or $\left(\sqrt[7]{\left(\frac35\right)}\right)^3$
Question 8
a) $16\sqrt2$
b) $24\sqrt3$
c) $40\sqrt5$
d) $128\sqrt2$
e) $16\sqrt[3]{256}$
f) $4374\sqrt[4]{8}$
Question 9
a) $\frac34$
b) $\frac{10}{3}$
c) $\frac{27}{8}$ or $3\frac38$
d) $\frac{1}{25}$
e) $\frac{49}{25}$
f) $\frac{32}{243}$
Solutions
Question 1
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b)
c)
d)
e)
f)
g)
h)
Question 2
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c)
d)
e)
f)
Question 3
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b)
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d)
e)
f)
g)
h)
Question 4
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d)
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f)
g)
h)
Question 5
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b)
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e)
f)
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j)
Question 6
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Question 7
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Question 8
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Question 9
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f)