Powers of a Power 3
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Question 1 of 4
1. Question
Simplify`(-2a^2 b^3)^4`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.$$(-2a^{\color{#007DDC}{2}}b^{\color{#007DDC}{3}})^{\color{#9a00c7}{4}}$$ `=` $$-2^{\color{#9a00c7}{4}}a^{\color{#007DDC}{2} \times \color{#9a00c7}{4}}b^{\color{#007DDC}{3} \times \color{#9a00c7}{4}}$$ `=` `16a^8 b^(12)` `16a^8 b^(12)` -
Question 2 of 4
2. Question
Simplify`[(2x^3)/(3y^2)]^3`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Simplify the expression by using the Power of a Power.$${\left[\frac{2x^{\color{#007DDC}{3}}}{3y^{\color{#007DDC}{2}}}\right]}^\color{#9a00c7}{3}$$ `=` $$\frac{2^{\color{#9a00c7}{3}}x^{\color{#007DDC}{3} \times \color{#9a00c7}{3}}}{3^{\color{#9a00c7}{3}}y^{\color{#007DDC}{2} \times \color{#9a00c7}{3}}}$$ `=` `(8x^9)/(27y^6)` `(8x^9)/(27y^6)` -
Question 3 of 4
3. Question
Simplify`((3x^5)^3)/((x^2)^4)`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$First, simplify the expression by using the Power of a Power.$$\frac{(3x^{\color{#007DDC}{5}})^{\color{#9a00c7}{3}}}{(x^{\color{#007DDC}{2}})^{\color{#9a00c7}{4}}}$$ `=` $$\frac{3^{\color{#9a00c7}{3}}x^{\color{#007DDC}{5} \times \color{#9a00c7}{3}}}{x^{\color{#007DDC}{2} \times \color{#9a00c7}{4}}}$$ `=` `(27x^15)/(x^8)` Simplify further using the Quotient of Powers.$$\frac{27\color{#00880A}{x}^{15}}{\color{#00880A}{x}^8}$$ `=` $$27\color{#00880A}{x}^{15-8}$$ `=` `27x^7` `27x^7` -
Question 4 of 4
4. Question
Simplify`((5a^2)/(6b))^3`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Simplify the expression by using the Power of a Power.$${\left(\frac{5a^{\color{#007DDC}{2}}}{6b}\right)}^\color{#9a00c7}{3}$$ `=` $$\frac{(5a^{\color{#007DDC}{2}})^{\color{#9a00c7}{3}}}{(6b)^{\color{#9a00c7}{3}}}$$ `=` $$\frac{5^{\color{#9a00c7}{3}}a^{\color{#007DDC}{2} \times \color{#9a00c7}{3}}}{6^{\color{#9a00c7}{3}}b^{\color{#9a00c7}{3}}}$$ `=` `(125a^6)/(216b^3)` `(125a^6)/(216b^3)`
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