Powers of a Power 1
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Question 1 of 5
1. Question
Simplify`(2^4)^3`Hint
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Fantastic!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Simplify the expression by using the Power of a Power.$${(2^{\color{#007DDC}{4}})}^\color{#9a00c7}{3}$$ `=` $$2^{{\color{#007DDC}{4}} \times {\color{#9a00c7}{3}}}$$ `=` `2^12` `2^12` -
Question 2 of 5
2. Question
Simplify`(a^3)^5`Hint
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Well Done!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Simplify the expression by using the Power of a Power.$${(a^{\color{#007DDC}{3}})}^\color{#9a00c7}{5}$$ `=` $$a^{{\color{#007DDC}{3}} \times {\color{#9a00c7}{5}}}$$ `=` `a^(15)` `a^(15)` -
Question 3 of 5
3. Question
Simplify`(x/y)^4`Hint
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Nice Job!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Simplify the expression by using the Power of a Power.$${\left(\frac{x^{\color{#007DDC}{1}}}{y^{\color{#004ec4}{1}}}\right)}^\color{#9a00c7}{4}$$ `=` $$\frac{x^{{\color{#007DDC}{1}} \times {\color{#9a00c7}{4}}}}{y^{{\color{#004ec4}{1}} \times {\color{#9a00c7}{4}}}}$$ `=` `(x^4)/(y^4)` `(x^4)/(y^4)` -
Question 4 of 5
4. Question
Simplify`(-6/m)^2`Hint
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Excellent!
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Simplify the expression by using the Power of a Power.$${\left(-\frac{6^{\color{#007DDC}{1}}}{m^{\color{#004ec4}{1}}}\right)}^\color{#9a00c7}{2}$$ `=` $$\frac{(-6)^{{\color{#007DDC}{1}} \times {\color{#9a00c7}{2}}}}{m^{{\color{#004ec4}{1}} \times {\color{#9a00c7}{2}}}}$$ `=` `((-6)^2)/(m^2)` `=` `(36)/(m^2)` `(-6)xx(-6)=36` `(36)/(m^2)` -
Question 5 of 5
5. Question
Simplify`(3xy)^2`Hint
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Exceptional!
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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.`(3xy)^2` `=` $$(3x^{\color{#007DDC}{1}}y^{\color{#007DDC}{1}})^{\color{#9a00c7}{2}}$$ `=` $$3^{\color{#9a00c7}{2}}x^{\color{#007DDC}{1} \times \color{#9a00c7}{2}} y^{\color{#007DDC}{1} \times \color{#9a00c7}{2}}$$ `=` `9x^2 y^2` `9x^2 y^2`
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