Multiply Exponents (Product Rule) 3

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Question 1 of 4

Simplify

3 y^{2} \times 4 y^{5}

$3y^2 xx 4y^5$

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

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Product of Powers

a^{m} \times a^{n} = a^{m + n}

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

First, bring the same bases together.

		$3 y^{2} \times 4 y^{5}$ $3y^2 xx 4y^5$
	$=$ $=$	$3 \times 4 \times y^{2} \times y^{5}$ $3 xx 4 xx y^2 xx y^5$

Using the Product of Powers, bring similar bases together.

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

12 y^{7}

$12y^7$

Question 2 of 4

Simplify

6 m^{7} \times 5 m^{3}

$6m^7 xx 5m^3$

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

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Product of Powers

a^{m} \times a^{n} = a^{m + n}

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

First, bring the same bases together.

		$6 m^{7} \times 5 m^{3}$ $6m^7 xx 5m^3$
	$=$ $=$	$6 \times 5 \times m^{7} \times m^{3}$ $6 xx 5 xx m^7 xx m^3$

Using the Product of Powers, bring similar bases together.

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

30 m^{10}

$30m^(10)$

Question 3 of 4

Simplify

6 m^{2} n \times 3 m^{4} n^{2}

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

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

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Product of Powers

a^{m} \times a^{n} = a^{m + n}

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

First, bring the same bases together.

		$6 m^{2} n \times 3 m^{4} n^{2}$ $6m^2 n xx 3m^4 n^2$
	$=$ $=$	$6 \times 3 \times m^{2} \times m^{4} \times n \times n^{2}$ $6 xx 3 xx m^2 xx m^4 xx n xx n^2$

Using the Product of Powers, bring similar bases together.

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

18 m^{6} n^{3}

$18m^6 n^3$

Question 4 of 4

Simplify

7 a b^{3} \times 2 a^{3} b

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

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

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Product of Powers

a^{m} \times a^{n} = a^{m + n}

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

First, bring the same bases together.

		$7 a b^{3} n \times 2 a^{3} b$ $7ab^3 n xx 2a^3 b$
	$=$ $=$	$7 \times 2 \times a \times a^{3} \times b^{3} \times b$ $7 xx 2 xx a xx a^3 xx b^3 xx b$

Using the Product of Powers, bring similar bases together.

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

14 a^{4} b^{4}

$14a^4 b^4$

Multiply Exponents (Product Rule) 3

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Quiz summary

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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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