Indices
UK Secondary (7-11)
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Power of a power with integer bases

Interactive practice questions

We want to simplify:

$\left(2^2\right)^4$(22)4

a

Select all of the expressions that are equivalent to $\left(2^2\right)^4$(22)4:

$2^2\times2^4$22×24

A

$\left(2\times2\right)^4$(2×2)4

B

$\left(2\times2\right)\times\left(2\times2\right)\times\left(2\times2\right)\times\left(2\times2\right)$(2×2)×(2×2)×(2×2)×(2×2)

C

$\left(2\times2\right)\times\left(2\times2\times2\times2\right)$(2×2)×(2×2×2×2)

D

$2^2\times2^2\times2^2\times2^2$22×22×22×22

E

$2^2\times2^4$22×24

A

$\left(2\times2\right)^4$(2×2)4

B

$\left(2\times2\right)\times\left(2\times2\right)\times\left(2\times2\right)\times\left(2\times2\right)$(2×2)×(2×2)×(2×2)×(2×2)

C

$\left(2\times2\right)\times\left(2\times2\times2\times2\right)$(2×2)×(2×2×2×2)

D

$2^2\times2^2\times2^2\times2^2$22×22×22×22

E
b

Choose the correct statement:

$\left(2^2\right)^4=2^{2\times4}$(22)4=22×4

A

$\left(2^2\right)^4=2^{2+4}$(22)4=22+4

B

$\left(2^2\right)^4=2^{2\times4}$(22)4=22×4

A

$\left(2^2\right)^4=2^{2+4}$(22)4=22+4

B
c

Fill in the box to complete the rule: $\left(2^2\right)^4=2^{\editable{}}$(22)4=2

Easy
Approx 2 minutes
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We want to simplify:

$\left(10^2\right)^3$(102)3

Express in simplified index form:

$\left(9^4\right)^3$(94)3

Express in simplified index form:

$\left(9^5\right)^7$(95)7

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