Negative Exponents 2

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Algebra 1

Exponents

Negative Exponents

Negative Exponents 2

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Question 1 of 5

1. Question
Simplify

${(\frac{4}{5})}^{- 3}$ $(4/5)^(-3)$

Write fractions as “a/b”
- (125/64)
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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.

${(\frac{4}{5})}^{- 3}$ $(4/5)^(-3)$ $=$ $=$ ${(\frac{5}{4})}^{3}$ $(5/4)^3$

$=$ $=$ $\frac{5^{3}}{4^{3}}$ $(5^3)/(4^3)$

$=$ $=$ $\frac{125}{64}$ $125/64$

$\frac{125}{64}$ $125/64$
Question 2 of 5

2. Question
Simplify

${(\frac{1}{m})}^{- 2} \times n^{- 3}$ $(1/m)^(-2) xx n^(-3)$
- 1. ${(\frac{n}{m})}^{6}$ $(n/m)^6$
- 2. $\frac{m^{2}}{n^{3}}$ $(m^2)/(n^3)$
- 3. $\frac{3 m}{n^{2}}$ $(3m)/(n^2)$
- 4. ${(\frac{m}{3 n})}^{2}$ $(m/(3n))^2$
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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.

${(\frac{1}{m})}^{- 2} \times n^{- 3}$ $(1/m)^(-2) xx n^(-3)$ $=$ $=$ ${(\frac{m}{1})}^{2} \times n^{- 3}$ $(m/1)^2 xx n^(-3)$

Use Negative Powers to simplify the expression.

$\left(\frac{m}{1}\right)^2 \times n^{\color{#e65021}{-3}}$ $=$ $=$ $\frac{m^2}{1^2} \times\frac{1}{n^{\color{#e65021}{3}}}$

$=$ $=$ $\frac{m^{2}}{n^{3}}$ $(m^2)/(n^3)$

$\frac{m^{2}}{n^{3}}$ $(m^2)/(n^3)$

Question 3 of 5

Simplify

{(a^{2} b^{- 2})}^{- 1}

$(a^2 b^(-2))^(-1)$

1. $a b^{2}$ $ab^2$
2. $\frac{b^{2}}{a^{2}}$ $(b^2)/(a^2)$
3. $\frac{a}{b^{2}}$ $a/(b^2)$
4. $2 a b$ $2ab$

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Power of a Power

{(a^{m})}^{n} = a^{m \times n}

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

Negative Powers

a^{- n} = \frac{1}{a^{n}}

$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$

Use Power of a Power and Negative Powers to simplify the expression.

${(a^{\color{#007DDC}{2}}b^{\color{#007DDC}{-2}})}^\color{#9a00c7}{-1}$	$=$ $=$	$a^{\color{#007DDC}{2} \times \color{#9a00c7}{-1}}b^{\color{#007DDC}{-2} \times \color{#9a00c7}{-1}}$
	$=$ $=$	$a^{\color{#e65021}{-2}}b^2$
	$=$ $=$	$\frac{1}{a^{\color{#e65021}{2}}} \times \frac{b^2}{1}$

	$=$ $=$	$\frac{b^{2}}{a^{2}}$ $(b^2)/(a^2)$

\frac{b^{2}}{a^{2}}

$(b^2)/(a^2)$

Question 4 of 5

Simplify

a^{2} (b^{- 3}) (a^{- 7})

$a^2(b^(-3))(a^(-7))$

1. $\frac{5 a}{3 b}$ $(5a)/(3b)$
2. $\frac{1}{b^{3} a^{5}}$ $1/(b^3 a^5)$
3. $\frac{a^{5}}{b^{3}}$ $(a^5)/(b^3)$
4. ${(\frac{a}{b})}^{9}$ $(a/b)^9$

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Negative Powers

a^{- n} = \frac{1}{a^{n}}

$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$

Quotient of Powers

a^{m} \div a^{n} = \frac{a^{m}}{a^{n}} = a^{m - n}

${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$

Use Negative Powers and Quotient of Powers to simplify the expression.

$a^2(b^{\color{#e65021}{-3}})(a^{\color{#e65021}{-7}})$	$=$ $=$	$a^2 \times \frac{1}{b^{\color{#e65021}{3}}} \times \frac{1}{a^{\color{#e65021}{7}}}$

	$=$ $=$	$\frac{\color{#00880A}{a}^2}{b^3 \times \color{#00880A}{a}^7}$

	$=$ $=$	$\frac{\color{#00880A}{a}^{2-7}}{b^3}$

	$=$ $=$	$\frac{a^{\color{#e65021}{-5}}}{b^3}$

	$=$ $=$	$\frac{1}{b^3 a^{\color{#e65021}{5}}}$

\frac{1}{b^{3} a^{5}}

$1/(b^3 a^5)$

Question 5 of 5

Simplify

{[\frac{9}{7 x}]}^{- 2}

$[9/(7x)]^(-2)$

1. $\frac{14 x}{21}$ $(14x)/21$
2. $\frac{14}{x}$ $14/x$
3. $\frac{49 x^{2}}{81}$ $(49x^2)/(81)$
4. $\frac{x}{81}$ $x/81$

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Power of a Power

{(a^{m})}^{n} = a^{m \times n}

${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$

Negative Powers

a^{- n} = \frac{1}{a^{n}}

$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$

A negative power means we flip a fraction and make the power positive.

${[\frac{9}{7 x}]}^{- 2}$ $[9/(7x)]^(-2)$	$=$ $=$	$\left[\frac{7x}{9}\right]^\color{#9a00c7}{2}$
	$=$ $=$	$\frac{7^{\color{#9a00c7}{2}}x^{\color{#9a00c7}{2}}}{9^{\color{#9a00c7}{2}}}$
	$=$ $=$	$\frac{49 x^{2}}{81}$ $(49x^2)/(81)$

\frac{49 x^{2}}{81}

$(49x^2)/(81)$

Negative Exponents 2

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Quiz summary

Information

1. Question

Hint

Exceptional!

Negative Powers

2. Question

Hint

Keep Going!

Negative Powers

3. Question

Hint

Correct!

Power of a Power

Negative Powers

4. Question

Hint

Great Work!

Negative Powers

Quotient of Powers

5. Question

Hint

Fantastic!

Power of a Power

Negative Powers

Quizzes

${(\frac{4}{5})}^{- 3}$ $(4/5)^(-3)$	$=$ $=$	${(\frac{5}{4})}^{3}$ $(5/4)^3$
	$=$ $=$	$\frac{5^{3}}{4^{3}}$ $(5^3)/(4^3)$
	$=$ $=$	$\frac{125}{64}$ $125/64$

$\left(\frac{m}{1}\right)^2 \times n^{\color{#e65021}{-3}}$	$=$ $=$	$\frac{m^2}{1^2} \times\frac{1}{n^{\color{#e65021}{3}}}$

	$=$ $=$	$\frac{m^{2}}{n^{3}}$ $(m^2)/(n^3)$