# Algebra - Indices

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## Question 1

Simplify each expression using indices

a) $x\times x$a s v d
b) $x\times x\times x$a s v d
c) $y\times y \times y\times y$a s v d
d) $t\times t\times t\times t\times t\times t\times t$a s v d
e) $q\times q\times q$a s v d
f) $p\times p\times p\times p\times p$a s v d
g) $3\times h\times h$a s v d
h) $7\times d\times d\times d$a s v d
i) $18\times z\times z\times z\times z\times z\times z$a s v d
j) $4\times k\times 3\times k$a s v d
k) $m\times 7\times 3\times m$a s v d
l) $2\times g\times g\times 3\times g$a s v d

## Question 2

Simplify each expression using indices

a) $7d\times d$a s v d
b) $9r\times 3\times r\times r$a s v d
c) $7u\times u\times u\times 4$a s v d
d) $2w\times 3w$a s v d
e) $5v\times v\times 3v$a s v d
f) $12c\times 3c\times c\times 2c$a s v d

## Question 3

Write each expression in the form $a^b$

a) $x^2\times x^3$a s v d
b) $h^3\times h^4$a s v d
c) $a^2\times a^5$a s v d
d) $n^4\times n^7$a s v d
e) $y^3\times y^1$a s v d
f) $y^3\times y$a s v d
g) $k\times k^2$a s v d
h) $r^3\times r^3$a s v d
i) $e^{11}\times e^4$a s v d
j) $t^{33}\times t^{21}$a s v d
k) $f^2\times g^3$a s v d

## Question 4

Write each expression in the form $a^b$

a) $w^4 \times w^{-1}$a s v d
b) $q^{-2}\times q^8$a s v d
c) $t^{-6}\times t^4$a s v d
d) $h^{-3} \times h^{-5}$a s v d
e) $r^{-10}\times r^{-4}$a s v d
f) $y^{33}\times y^{-21}$a s v d
g) $v^{-67}\times v^{-16}$a s v d

## Question 5

Write each expression in the form $a^b$

a) $x^{\frac15}\times x^{\frac25}$a s v d
b) $z^{\frac19}\times z^{\frac49}$a s v d
c) $h^{\frac{5}{11}}\times h^{\frac{5}{11}}$a s v d
d) $s^{\frac13}\times s^{\frac12}$a s v d
e) $u^{\frac14}\times u^{\frac15}$a s v d
f) $a^{\frac12}\times a$a s v d
g) $p^{\frac34}\times p^{\frac12}$a s v d
h) $c^{2}\times c^{\frac35}$a s v d
i) $g^{\frac54}\times g^{\frac74}$a s v d
j) $m^{\frac35}\times m^{\frac56}$a s v d
k) $b^{-\frac32}\times b^{\frac45}$a s v d

## Question 6

Write each expression in the form $a^b$

a) $x^6\div x^2$a s v d
b) $y^7\div y^3$a s v d
c) $s^9\div s^4$a s v d
d) $w^4\div w^3$a s v d
e) $r^{13}\div r^5$a s v d
f) $d^{17}\div d^{14}$a s v d
g) $t^3\div t^5$a s v d
h) $p^2\div p^7$a s v d

## Question 7

Write each expression in the form $a^b$

a) $u^{-3}\div u^4$a s v d
b) $k^{-4}\div k^6$a s v d
c) $h^{-4}\div h^{-1}$a s v d
d) $e^{-7}\div e^{-2}$a s v d
e) $g^{-2}\div g^{-5}$a s v d
f) $v^{-6}\div v^{-10}$a s v d
g) $q^{-14}\div q^{-23}$a s v d

## Question 8

Write each expression in the form $a^b$

a) $x^{\frac57}\div x^{\frac27}$a s v d
b) $z^{\frac59}\div z^{\frac49}$a s v d
c) $p^{\frac{12}{5}}\div p^{\frac{8}{5}}$a s v d
d) $g^{\frac13}\div g^{\frac14}$a s v d
e) $d^{\frac15}\div d^{\frac19}$a s v d
f) $a^{\frac34}\div a^{\frac12}$a s v d
g) $u^{\frac23}\div u^{\frac16}$a s v d
h) $n^{\frac65}\div n^{\frac34}$a s v d
i) $y^3\div y^{\frac76}$a s v d
j) $b^{-\frac23}\div b^2$a s v d
k) $j^{-\frac65}\div j^{-\frac92}$a s v d

## Question 9

Write each expression in the form $a^b$

a) $\frac{x^5}{x^2}$a s v d
b) $\frac{y^7}{x^3}$a s v d
c) $\frac{r^{15}}{r^8}$a s v d
d) $\frac{q^{3.2}}{q^{1.2}}$a s v d
e) $\frac{t^{-3}}{t^2}$a s v d
f) $\frac{a^{3}}{a^{-5}}$a s v d
g) $\frac{g^{-5}}{g^{-2}}$a s v d
h) $\frac{e^{-4}}{e^{-4}}$a s v d
i) $\frac{p^{\frac45}}{p^{\frac35}}$a s v d
j) $\frac{q^{\frac67}}{q^{\frac47}}$a s v d
k) $\frac{h^{\frac12}}{h^{\frac13}}$a s v d
l) $\frac{m^{\frac56}}{m^{-\frac23}}$a s v d

## Question 10

Write each expression in the form $a^b$

a) ${(x^2)}^3$a s v d
b) ${(w^3)}^5$a s v d
c) ${(u^4)}^7$a s v d
d) ${(f^3)}^9$a s v d
e) ${(e^7)}^2$a s v d
f) ${(m^{10})}^3$a s v d
g) ${(h^{14})}^4$a s v d
h) ${(z^{17})}^7$a s v d

## Question 11

Write each expression in the form $a^b$

a) ${(k^2)}^{-3}$a s v d
b) ${(n^{-4})}^2$a s v d
c) ${(t^{-5})}^6$a s v d
d) ${(z^7)}^{-2}$a s v d
e) ${(c^{-2})}^{-5}$a s v d
f) ${(g^{-6})}^{-3}$a s v d
g) ${(q^{5})}^{-2}$a s v d
h) ${(s^{-14})}^{-8}$a s v d

## Question 12

Write each expression in the form $a^b$

a) ${\left(x^{\frac12}\right)}^{\frac13}$a s v d
b) ${\left(j^{\frac23}\right)}^{\frac15}$a s v d
c) ${\left(p^{\frac14}\right)}^{\frac23}$a s v d
d) ${\left(w^{\frac54}\right)}^{\frac12}$a s v d
e) ${\left(y^{\frac34}\right)}^{\frac12}$a s v d
f) ${\left(u^{\frac67}\right)}^{\frac23}$a s v d
g) ${\left(x^{-\frac35}\right)}^{\frac12}$a s v d
h) ${\left(q^{\frac37}\right)}^{\frac78}$a s v d
i) ${\left(e^{\frac43}\right)}^{-\frac67}$a s v d
j) ${\left(n^{-\frac{16}{15}}\right)}^{-\frac34}$a s v d

## Question 13

Simplify each expression using indices

a) $x^2\times x^4\times x^3$a s v d
b) $p^3\times p^5\times p^2$a s v d
c) $w^{-3}\times w^2\times w^8$a s v d
d) $g^{-2}\times g\times g^{-3}\times g$a s v d
e) $4d^2\times d^3\times 2\times d^{-1}$a s v d
f) ${(p^2)}^3 \times p^4$a s v d
g) ${(y^3)}^5 \times {(y^2)}^4$a s v d
h) ${(2p^3)}^3$a s v d
i) ${(5e^5)}^2$a s v d
j) ${(f^2)}^3\times {(2f)}^2$a s v d
k) $\frac{x^6}{\frac{x^5}{x^4}}$a s v d
l) $h^3\times h^6\div h^4$a s v d
m) $k^3\div k^6\times k^5$a s v d
n) ${\left({\frac{w^{18}}{w^{12}}}\right)}^2$a s v d
o) ${\left({\frac{c}{c^{-1}}}\right)}^3$a s v d
p) $4\times{\left({\frac{u^{-2}}{u^{-2}}}\right)}^8\times 2u^5\div u^{-3}$a s v d
q) ${\left({\frac{\frac{n^{-7}}{n^2}}{\frac{n^2}{n^4}}}\right)}^{-7}$a s v d
r) $5t^2\times{\left({\frac{\frac{t^{-3}}{t^-4}}{\frac{t^{-7}}{t^{-1}}}}\right)}^{-15}\times4$a s v d