# Power of a power with variable bases

## Interactive practice questions

We want to simplify:

$\left(r^2\right)^4$(r2)4

a

Select all of the expressions that are equivalent to $\left(r^2\right)^4$(r2)4:

$r^2\times r^4$r2×r4

A

$\left(r\times r\right)\times\left(r\times r\times r\times r\right)$(r×r)×(r×r×r×r)

B

$\left(r\times r\right)^4$(r×r)4

C

$\left(r\times r\right)\times\left(r\times r\right)\times\left(r\times r\right)\times\left(r\times r\right)$(r×r)×(r×r)×(r×r)×(r×r)

D

$r^2\times r^2\times r^2\times r^2$r2×r2×r2×r2

E

$r^2\times r^4$r2×r4

A

$\left(r\times r\right)\times\left(r\times r\times r\times r\right)$(r×r)×(r×r×r×r)

B

$\left(r\times r\right)^4$(r×r)4

C

$\left(r\times r\right)\times\left(r\times r\right)\times\left(r\times r\right)\times\left(r\times r\right)$(r×r)×(r×r)×(r×r)×(r×r)

D

$r^2\times r^2\times r^2\times r^2$r2×r2×r2×r2

E
b

Choose the correct statement:

$\left(r^2\right)^4=r^{2+4}$(r2)4=r2+4

A

$\left(r^2\right)^4=r^{2\times4}$(r2)4=r2×4

B

$\left(r^2\right)^4=r^{2+4}$(r2)4=r2+4

A

$\left(r^2\right)^4=r^{2\times4}$(r2)4=r2×4

B
c

Fill in the box to complete the rule: $\left(r^2\right)^4=r^{\editable{}}$(r2)4=r

Easy
Approx a minute

Simplify the following, giving your answer with a positive exponent: $\left(w^3\right)^4$(w3)4

Express the following in simplified exponential form:

$\left(j^2\right)^5$(j2)5

Express the following in simplified exponential form:

$\left(c^9\right)^2$(c9)2

### Outcomes

#### 9D.NA1.04

Extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents