Powers of a Power 2

Years

Year 8

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Powers of a Power

Powers of a Power 2

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Question 1 of 5

1. Question
Simplify

$(4a^3)^2$
- 1. $16a^6$
- 2. $6a^5$
- 3. $4a^6$
- 4. $16a$
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Power of a Power

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

Apply the power of a power to all terms inside the bracket, then simplify.

$(4a^3)^2$ $=$ $(4a^{\color{#007DDC}{3}})^{\color{#9a00c7}{2}}$

$=$ $4^{\color{#9a00c7}{2}}a^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}$

$=$ $16a^6$

$16a^6$

Question 2 of 5

Simplify

$[(-2m)^2]^3$

1. $64m^6$
2. $4m^5$
3. $-8m^2$
4. $-4m^3$

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Power of a Power

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

First, apply the power of a power to all terms inside the parenthesis, then simplify.

$[(-2m)^2]^3$	$=$	$[(-2m^{\color{#007DDC}{1}})^{\color{#9a00c7}{2}}]^3$
	$=$	$[-2^{\color{#9a00c7}{2}}m^{\color{#007DDC}{1} \times \color{#9a00c7}{2}}]^3$
	$=$	$[4m^2]^3$

Next, simplify further by applying the power of a power to all terms inside the bracket.

$[4m^{\color{#007DDC}{2}}]^{\color{#9a00c7}{3}}$	$=$	$4^{\color{#9a00c7}{3}}m^{\color{#007DDC}{2} \times \color{#9a00c7}{3}}$
	$=$	$64m^6$

$64m^6$

Question 3 of 5

Simplify

$(a^2 b^3)^5$

1. $a^(10) b^(15)$
2. $5ab^15$
3. $5a^2b^3$
4. $5a^7b^8$

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Power of a Power

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

Apply the power of a power to all terms inside the bracket, then simplify.

$(a^{\color{#007DDC}{2}}b^{\color{#007DDC}{3}})^{\color{#9a00c7}{5}}$	$=$	$a^{\color{#007DDC}{2} \times \color{#9a00c7}{5}}b^{\color{#007DDC}{3} \times \color{#9a00c7}{5}}$
	$=$	$a^(10) b^(15)$

$a^(10) b^(15)$

Question 4 of 5

4. Question
Simplify

$2(4m^2)^3$
- 1. $128m^6$
- 2. $64m^3$
- 3. $4m^3$
- 4. $8m^6$
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Power of a Power

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

Apply the power of a power to all terms inside the bracket, then simplify.

$2(4m^{\color{#007DDC}{2}})^{\color{#9a00c7}{3}}$ $=$ $2(4^{\color{#9a00c7}{3}}m^{\color{#007DDC}{2} \times \color{#9a00c7}{3}})$

$=$ $2(64m^6)$

$=$ $128m^6$

$128m^6$

Question 5 of 5

Simplify

$(x^4 y^8)^(1/2)$

1. $x^4 y^4$
2. $(xy^4)/2$
3. $x^2 y^4$
4. $(4xy)/2$

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Power of a Power

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

Apply the power of a power to all terms inside the bracket, then simplify.

$(x^{\color{#007DDC}{4}}y^{\color{#007DDC}{8}})^{\color{#9a00c7}{\frac{1}{2}}}$	$=$	$x^{\color{#007DDC}{4} \times \color{#9a00c7}{\frac{1}{2}}}b^{\color{#007DDC}{8} \times \color{#9a00c7}{\frac{1}{2}}}$
	$=$	$x^(4/2) y^(8/2)$
	$=$	$x^2 y^4$

$x^2 y^4$

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Quiz summary

Information

1. Question

Hint

Fantastic!

Power of a Power

2. Question

Hint

Keep Going!

Power of a Power

3. Question

Hint

Correct!

Power of a Power

4. Question

Hint

Great Work!

Power of a Power

5. Question

Hint

Correct!

Power of a Power

Quizzes

$(4a^3)^2$	$=$	$(4a^{\color{#007DDC}{3}})^{\color{#9a00c7}{2}}$
	$=$	$4^{\color{#9a00c7}{2}}a^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}$
	$=$	$16a^6$

$2(4m^{\color{#007DDC}{2}})^{\color{#9a00c7}{3}}$	$=$	$2(4^{\color{#9a00c7}{3}}m^{\color{#007DDC}{2} \times \color{#9a00c7}{3}})$
	$=$	$2(64m^6)$
	$=$	$128m^6$