Powers of a Power 2
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Question 1 of 5
1. Question
Simplify`(4a^3)^2`Hint
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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
2. Question
Simplify`[(-2m)^2]^3`Hint
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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
3. Question
Simplify`(a^2 b^3)^5`Hint
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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`Hint
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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
5. Question
Simplify`(x^4 y^8)^(1/2)`Hint
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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`
Quizzes
- Index Notation 1
- Index Notation 2
- Index Notation 3
- Multiply Indices 1
- Multiply Indices 2
- Multiply Indices 3
- Multiply Indices 4
- Divide Indices 1
- Divide Indices 2
- Powers of a Power 1
- Powers of a Power 2
- Powers of a Power 3
- Powers of a Power 4
- Zero Powers 1
- Zero Powers 2
- Negative Indices 1
- Negative Indices 2
- Negative Indices 3
- Fractional Indices 1
- Fractional Indices 2
- Fractional Indices 3
- Mixed Operations with Indices 1
- Mixed Operations with Indices 2