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Grade 12

Power of a power with variable bases

Interactive practice questions

We want to simplify:

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

a

Select the three expressions which 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
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
c

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

Easy
1min

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

Easy
< 1min

Express the following in simplified exponential form:

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

Easy
< 1min

Express the following in simplified exponential form:

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

Easy
< 1min
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Outcomes

12C.A.1.1

Determine, through investigation (e.g., by expanding terms and patterning), the exponent laws for multiplying and dividing algebraic expressions involving exponents and the exponent law for simplifying algebraic expressions involving a power of a power

12C.A.1.2

Simplify algebraic expressions containing integer exponents using the laws of exponents

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