Number - Fractional Indices Questions

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Question 1


Evaluate:

a) $9^{\frac12}$a s v d
b) $8^{\frac13}$a s v d
c) $81^{\frac14}$a s v d
d) $16^{\frac12}$a s v d
e) $32^{\frac15}$a s v d
f) $1000^{\frac13}$a s v d
g) $64^{\frac16}$a s v d
h) $1^{\frac15}$a s v d


Question 2


Evaluate:

a) $\left(\frac{1}{100}\right)^{\frac12}$a s v d
b) $\left(\frac{1}{8}\right)^{\frac13}$a s v d
c) $\left(\frac{1}{81}\right)^{\frac14}$a s v d
d) $\left(\frac{1}{125}\right)^{\frac13}$a s v d
e) $\left(\frac{1}{49}\right)^{\frac12}$a s v d
f) $\left(\frac{1}{256}\right)^{\frac14}$a s v d


Question 3


Evaluate:

a) $\left(\frac{9}{16}\right)^{\frac12}$a s v d
b) $\left(\frac{8}{27}\right)^{\frac13}$a s v d
c) $\left(\frac{16}{81}\right)^{\frac14}$a s v d
d) $\left(\frac{16}{81}\right)^{\frac12}$a s v d
e) $\left(\frac{27}{125}\right)^{\frac13}$a s v d
f) $\left(\frac{81}{4}\right)^{\frac12}$a s v d
g) $\left(\frac{1000}{27}\right)^{\frac13}$a s v d
h) $\left(\frac{121}{16}\right)^{\frac12}$a s v d


Question 4


Evaluate:

a) $9^{\frac32}$a s v d
b) $16^{\frac32}$a s v d
c) $4^{\frac52}$a s v d
d) $27^{\frac23}$a s v d
e) $16^{\frac34}$a s v d
f) $1000^{\frac53}$a s v d
g) $32^{\frac65}$a s v d
h) $125^{\frac43}$a s v d


Question 5


Evaluate, leaving your answers as surds where necessary.

a) $2^{\frac12}$a s v d
b) $10^{\frac12}$a s v d
c) $5^{\frac13}$a s v d
d) $7^{\frac14}$a s v d
e) $\left(\frac35\right)^{\frac12}$a s v d
f) $\left(\frac17\right)^{\frac12}$a s v d
g) $\left(\frac45\right)^{\frac12}$a s v d
h) $\left(\frac79\right)^{\frac12}$a s v d
i) $\left(\frac83\right)^{\frac13}$a s v d
j) $\left(\frac{81}{9}\right)^{\frac14}$a s v d


Question 6


Evaluate, leaving your answers as surds where necessary.

a) $2^{\frac32}$a s v d
b) $3^{\frac32}$a s v d
c) $5^{\frac52}$a s v d
d) $7^{\frac43}$a s v d
e) $11^{\frac73}$a s v d
f) $1^{\frac54}$a s v d


Question 7


Evaluate, leaving your answers as surds where necessary.

a) $5^{\frac23}$a s v d
b) $13^{\frac23}$a s v d
c) $3^{\frac45}$a s v d
d) $21^{\frac74}$a s v d
e) $9^{\frac23}$a s v d
f) $4^{\frac43}$a s v d
g) $16^{\frac75}$a s v d
h) $\left(\frac35\right)^{\frac37}$a s v d


Question 8


Evaluate, leaving your answers as simplified surds where necessary.

a) $8^{\frac32}$a s v d
b) $12^{\frac32}$a s v d
c) $20^{\frac32}$a s v d
d) $8^{\frac52}$a s v d
e) $16^{\frac53}$a s v d
f) $162^{\frac74}$a s v d


Question 9


Evaluate:

a) $\left(\frac{9}{16}\right)^{\frac{1}{3}}\times\left(\frac{9}{16}\right)^{\frac{1}{6}}$a s v d
b) $\left(\frac{1000}{27}\right)^{\frac{1}{5}}\times\left(\frac{1000}{27}\right)^{\frac{2}{15}}$a s v d
c) $\left(5\frac{1}{16}\right)^{\frac{7}{10}}\times\left(5\frac{1}{16}\right)^{\frac{1}{20}}$a s v d
d) $\left(\frac{1}{3125}\right)^{\frac{1}{2}}\div\left(\frac{1}{3125}\right)^{0.1}$a s v d
e) $\left(\left(\frac{343}{125}\right)^{\frac{1}{9}}\right)^6$a s v d
f) $\sqrt{\frac{\left(0.\dot4\right)^{31}}{\left(\frac{16}{81}\right)^{13}}}$a s v d