Negative Indices 2
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Question 1 of 5
1. Question
Simplify`(4/5)^(-3)`Write fractions as “a/b”- (125/64)
Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$A negative power means we flip a fraction and make the power positive.`(4/5)^(-3)` `=` `(5/4)^3` `=` `(5^3)/(4^3)` `=` `125/64` `125/64` -
Question 2 of 5
2. Question
Simplify`(1/m)^(-2) xx n^(-3)`Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$A negative power means we flip a fraction and make the power positive.`(1/m)^(-2) xx n^(-3)` `=` `(m/1)^2 xx n^(-3)` Use Negative Powers to simplify the expression.$$\left(\frac{m}{1}\right)^2 \times n^{\color{#e65021}{-3}}$$ `=` $$\frac{m^2}{1^2} \times\frac{1}{n^{\color{#e65021}{3}}}$$ `=` `(m^2)/(n^3)` `(m^2)/(n^3)` -
Question 3 of 5
3. Question
Simplify`(a^2 b^(-2))^(-1)`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Use Power of a Power and Negative Powers to simplify the expression.$${(a^{\color{#007DDC}{2}}b^{\color{#007DDC}{-2}})}^\color{#9a00c7}{-1}$$ `=` $$a^{\color{#007DDC}{2} \times \color{#9a00c7}{-1}}b^{\color{#007DDC}{-2} \times \color{#9a00c7}{-1}}$$ `=` $$a^{\color{#e65021}{-2}}b^2$$ `=` $$\frac{1}{a^{\color{#e65021}{2}}} \times \frac{b^2}{1}$$ `=` `(b^2)/(a^2)` `(b^2)/(a^2)` -
Question 4 of 5
4. Question
Simplify`a^2(b^(-3))(a^(-7))`Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Use Negative Powers and Quotient of Powers to simplify the expression.$$a^2(b^{\color{#e65021}{-3}})(a^{\color{#e65021}{-7}})$$ `=` $$a^2 \times \frac{1}{b^{\color{#e65021}{3}}} \times \frac{1}{a^{\color{#e65021}{7}}}$$ `=` $$\frac{\color{#00880A}{a}^2}{b^3 \times \color{#00880A}{a}^7}$$ `=` $$\frac{\color{#00880A}{a}^{2-7}}{b^3}$$ `=` $$\frac{a^{\color{#e65021}{-5}}}{b^3}$$ `=` $$\frac{1}{b^3 a^{\color{#e65021}{5}}}$$ `1/(b^3 a^5)` -
Question 5 of 5
5. Question
Simplify`[9/(7x)]^(-2)`Hint
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Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$A negative power means we flip a fraction and make the power positive.`[9/(7x)]^(-2)` `=` $$\left[\frac{7x}{9}\right]^\color{#9a00c7}{2}$$ `=` $$\frac{7^{\color{#9a00c7}{2}}x^{\color{#9a00c7}{2}}}{9^{\color{#9a00c7}{2}}}$$ `=` `(49x^2)/(81)` `(49x^2)/(81)`
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