Multiply Indices 3

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Question 1 of 4

Simplify

$3y^2 xx 4y^5$

1. $12y^3$
2. $y^7$
3. $7y^5$
4. $12y^7$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, bring the same bases together.

		$3y^2 xx 4y^5$
	$=$	$3 xx 4 xx y^2 xx y^5$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{3}^1 \times \color{#00880A}{4}^1 \times \color{#9a00c7}{y}^2 \times \color{#9a00c7}{y}^5$	$=$	$\color{#00880A}{12} \times \color{#9a00c7}{y}^{2+5}$
	$=$	$12y^7$

$12y^7$

Question 2 of 4

Simplify

$6m^7 xx 5m^3$

1. $30m^4$
2. $30m^(10)$
3. $m^10$
4. $m^4$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, bring the same bases together.

		$6m^7 xx 5m^3$
	$=$	$6 xx 5 xx m^7 xx m^3$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{6}^1 \times \color{#00880A}{5}^1 \times \color{#9a00c7}{m}^7 \times \color{#9a00c7}{m}^3$	$=$	$\color{#00880A}{30} \times \color{#9a00c7}{m}^{7+3}$
	$=$	$30m^(10)$

$30m^(10)$

Question 3 of 4

Simplify

$6m^2 n xx 3m^4 n^2$

1. $18m^6 n^3$
2. $18mn^3$
3. $3m^2 n$
4. $9m^6 n^3$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, bring the same bases together.

		$6m^2 n xx 3m^4 n^2$
	$=$	$6 xx 3 xx m^2 xx m^4 xx n xx n^2$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{6}^1 \times \color{#00880A}{3}^1 \times \color{#9a00c7}{m}^2 \times \color{#9a00c7}{m}^4 \times \color{#e65021}{n}^1 \times \color{#e65021}{n}^2$	$=$	$\color{#00880A}{18} \times \color{#9a00c7}{m}^{2+4} \times \color{#e65021}{n}^{1+2}$
	$=$	$18m^6 n^3$

$18m^6 n^3$

Question 4 of 4

Simplify

$7ab^3 xx 2a^3 b$

1. $9a^4 b$
2. $14a^2b^2$
3. $5ab^4$
4. $14a^4 b^4$

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Product of Powers

${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$

First, bring the same bases together.

		$7ab^3 n xx 2a^3 b$
	$=$	$7 xx 2 xx a xx a^3 xx b^3 xx b$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{7}^1 \times \color{#00880A}{2}^1 \times \color{#9a00c7}{a}^1 \times \color{#9a00c7}{a}^3 \times \color{#e65021}{b}^3 \times \color{#e65021}{b}^1$	$=$	$\color{#00880A}{14} \times \color{#9a00c7}{a}^{1+3} \times \color{#e65021}{b}^{3+1}$
	$=$	$14a^4 b^4$

$14a^4 b^4$

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Quiz summary

Information

1. Question

Hint

Correct!

Product of Powers

2. Question

Hint

Nice Job!

Product of Powers

3. Question

Hint

Keep Going!

Product of Powers

4. Question

Hint

Excellent!

Product of Powers

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