Indices

UK Secondary (7-11)

Power of a power with variable bases

We want to simplify:

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

a

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

$r^2\times r^4$`r`2×`r`4

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

$r^2\times r^2\times r^2\times r^2$`r`2×`r`2×`r`2×`r`2

E

$r^2\times r^4$`r`2×`r`4

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

$r^2\times r^2\times r^2\times r^2$`r`2×`r`2×`r`2×`r`2

E

b

Choose the correct statement:

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

A

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

B

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

A

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

B

c

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

Easy

Approx a minute

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