Multiply Exponents (Product Rule) 2

Topics

Algebra 1

Exponents

Multiply Exponents (Product Rule)

Multiply Exponents (Product Rule) 2

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Question 1 of 5

1. Question
Simplify

$2^{1} \times 2^{7} \times 2^{4}$ $2^1 xx 2^7 xx 2^4$
- 1. $2^{4}$ $2^4$
- 2. $12$ $12$
- 3. $2^{8}$ $2^8$
- 4. $2^{12}$ $2^12$
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Product of Powers

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

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{2}^1 \times \color{#00880A}{2}^7 \times \color{#00880A}{2}^4$ $=$ $=$ $\color{#00880A}{2}^{1+7+4}$

$=$ $=$ $2^{12}$ $2^12$

$2^{12}$ $2^12$
Question 2 of 5

2. Question
Simplify

$a^{3} \times a^{4} \times a^{- 2}$ $a^3 xx a^4 xx a^(-2)$
- 1. $a^{9}$ $a^9$
- 2. $\frac{a^{7}}{a}$ $(a^7)/a$
- 3. $a^{5}$ $a^5$
- 4. $2 a^{7}$ $2a^7$
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Product of Powers

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

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{a}^3 \times \color{#00880A}{a}^4 \times \color{#00880A}{a}^{-2}$ $=$ $=$ $\color{#00880A}{a}^{3+4+(-2)}$

$=$ $=$ $a^{5}$ $a^5$

$a^{5}$ $a^5$

Question 3 of 5

Simplify

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

$m^3 n xx mn^4$

1. $m^{4} n^{5}$ $m^4 n^5$
2. $m n^{4} m n^{5}$ $mn^4 mn^5$
3. $m^{2} n^{3}$ $m^2 n^3$
4. $4 m 5 n$ $4m5n$

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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.

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

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{m}^3 \times \color{#00880A}{m}^1 \times \color{#9a00c7}{n}^1 \times \color{#9a00c7}{n}^4$	$=$ $=$	$\color{#00880A}{m}^{3+1} \times \color{#9a00c7}{n}^{1+4}$
	$=$ $=$	$m^{4} n^{5}$ $m^4 n^5$

m^{4} n^{5}

$m^4 n^5$

Question 4 of 5

Simplify

x y z \times x^{2} z

$xyz xx x^2 z$

1. $x^{3} y z^{2}$ $x^3 yz^2$
2. $x^{2} y^{2} z^{3}$ $x^2 y^2 z^3$
3. $x^{3} y^{2} z$ $x^3 y^2 z$
4. $3 x y^{2} 2 z$ $3xy^2 2z$

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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.

		$x y z \times x^{2} z$ $xyz xx x^2 z$
	$=$ $=$	$x \times x^{2} \times y \times z \times z$ $x xx x^2 xx y xx z xx z$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{x}^1 \times \color{#00880A}{x}^2 \times \color{#9a00c7}{y}^1 \times \color{#e65021}{z}^1 \times \color{#e65021}{z}^1$	$=$ $=$	$\color{#00880A}{x}^{1+2} \times \color{#9a00c7}{y}^{1} \times \color{#e65021}{z}^{1+1}$
	$=$ $=$	$x^{3} y z^{2}$ $x^3 yz^2$

x^{3} y z^{2}

$x^3 yz^2$

Question 5 of 5

Simplify

3 y^{2} \times 5 y

$3y^2 xx 5y$

1. $3 y^{5}$ $3y^5$
2. $5 y^{3}$ $5y^3$
3. $15 y^{5}$ $15y^5$
4. $15 y^{3}$ $15y^3$

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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.

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

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{3}^1 \times \color{#00880A}{5}^1 \times \color{#9a00c7}{y}^2 \times \color{#9a00c7}{y}^1$	$=$ $=$	$\color{#00880A}{15} \times \color{#9a00c7}{y}^{2+1}$
	$=$ $=$	$15 y^{3}$ $15y^3$

15 y^{3}

$15y^3$

Multiply Exponents (Product Rule) 2

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Quiz summary

Information

1. Question

Hint

Great Work!

Product of Powers

2. Question

Hint

Great Work!

Product of Powers

3. Question

Hint

Correct!

Product of Powers

4. Question

Hint

Great Work!

Product of Powers

5. Question

Hint

Well Done!

Product of Powers

Quizzes

$\color{#00880A}{2}^1 \times \color{#00880A}{2}^7 \times \color{#00880A}{2}^4$	$=$ $=$	$\color{#00880A}{2}^{1+7+4}$
	$=$ $=$	$2^{12}$ $2^12$

$\color{#00880A}{a}^3 \times \color{#00880A}{a}^4 \times \color{#00880A}{a}^{-2}$	$=$ $=$	$\color{#00880A}{a}^{3+4+(-2)}$
	$=$ $=$	$a^{5}$ $a^5$