Negative Indices 1
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Question 1 of 6
1. Question
Simplify`3^(-2)`Write fractions as “a/b”- (1/9)
Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$Use Negative Powers to simplify the expression.$$3^{\color{#e65021}{-2}}$$ `=` $$\frac{1}{3^{\color{#e65021}{2}}}$$ `=` `1/9` `1/9` -
Question 2 of 6
2. Question
Simplify`x^(-5)`Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$Use Negative Powers to simplify the expression.$$x^{\color{#e65021}{-5}}$$ `=` $$\frac{1}{x^{\color{#e65021}{5}}}$$ `1/(x^5)` -
Question 3 of 6
3. Question
Simplify`a^2 b^(-3)`Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$First, separate the bases..`a^2 b^(-3)` `=` `a^2 xx b^(-3)` Now use Negative Powers to simplify the expression.$$a^2 \times b^{\color{#e65021}{-3}}$$ `=` $$a^2 \times \frac{1}{b^{\color{#e65021}{3}}}$$ `=` `(a^2)/(b^3)` `(a^2)/(b^3)` -
Question 4 of 6
4. Question
Simplify`(1/5)^(-2)`- (25)
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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.`(1/5)^(-2)` `=` `(5/1)^2` `=` `5^2` `=` `25` `25` -
Question 5 of 6
5. Question
Simplify`1/(4^(-3))`- (64)
Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$The negative power on the denominator can be written as a power for the whole fraction.`1/(4^(-3))` `=` `(1/4)^(-3)` A negative power means we flip a fraction and make the power positive.`(1/4)^(-3)` `=` `(4/1)^3` `=` `4^2` `=` `64` `64` -
Question 6 of 6
6. Question
Simplify`(6x)^(-2)`Hint
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Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$Use Negative Powers to simplify the expression.$${(6x)}^{\color{#e65021}{-2}}$$ `=` $$\frac{1}{{(6x)}^{\color{#e65021}{2}}}$$ Consider bracketed terms together `=` $$\frac{1}{6^{\color{#e65021}{2}} \times x^{\color{#e65021}{2}}}$$ Apply the power to all items in the bracket `=` `1/(36x^2)` `1/(36x^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