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

Help Video

Correct

Exceptional!

Incorrect

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

$(1/m)^(-2) xx n^(-3)$
- 1. $(m/(3n))^2$
- 2. $(3m)/(n^2)$
- 3. $(m^2)/(n^3)$
- 4. $(n/m)^6$
Hint

Help Video

Correct

Keep Going!

Incorrect

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

Simplify

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

1. $a/(b^2)$
2. $(b^2)/(a^2)$
3. $2ab$
4. $ab^2$

Incorrect

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

Simplify

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

1. $1/(b^3 a^5)$
2. $(a^5)/(b^3)$
3. $(a/b)^9$
4. $(5a)/(3b)$

Incorrect

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

$[9/(7x)]^(-2)$
- 1. $(14x)/21$
- 2. $(49x^2)/(81)$
- 3. $14/x$
- 4. $x/81$
Hint

Help Video

Correct

Fantastic!

Incorrect

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.

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

$=$ $\frac{7^{\color{#9a00c7}{2}}x^{\color{#9a00c7}{2}}}{9^{\color{#9a00c7}{2}}}$

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

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

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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

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

	$=$	$(m^2)/(n^3)$

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

$(4/5)^(-3)$	$=$	$(5/4)^3$
	$=$	$(5^3)/(4^3)$
	$=$	$125/64$