Multiply Exponents (Product Rule) 4

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Question 1 of 3

Simplify

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

$5m^(-2) n^4 xx 3m^6 n^(-3)$

1. $2 m^{6} n^{7}$ $2m^6 n^7$
2. $8 m^{4} n^{2}$ $8m^4 n^2$
3. $15 m^{- 4} n$ $15m^(-4) n$
4. $15 m^{4} n$ $15m^4 n$

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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.

		$5 m^{- 2} n^{4} \times 3 m^{6} n^{- 3}$ $5m^(-2) n^4 xx 3m^6 n^(-3)$
	$=$ $=$	$5 \times 3 \times m^{- 2} \times m^{6} \times n^{4} \times n^{- 3}$ $5 xx 3 xx m^(-2) xx m^6 xx n^4 xx n^(-3)$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{5}^1 \times \color{#00880A}{3}^1 \times \color{#9a00c7}{m}^{-2} \times \color{#9a00c7}{m}^6 \times \color{#e65021}{n}^4 \times \color{#e65021}{n}^{-3}$	$=$ $=$	$\color{#00880A}{15} \times \color{#9a00c7}{m}^{(-2)+6} \times \color{#e65021}{n}^{4+(-3)}$
	$=$ $=$	$15 m^{4} n$ $15m^4 n$

15 m^{4} n

$15m^4 n$

Question 2 of 3

Simplify

(6 x y^{4}) (- 2 x^{3} y^{2})

$(6xy^4)(-2x^3 y^2)$

1. $12 x^{2} y^{2}$ $12x^2 y^2$
2. $- 6 x^{2} y^{6}$ $-6x^2 y^6$
3. $- 12 x^{4} y^{6}$ $-12x^4 y^6$
4. $6 x^{4} y^{6}$ $6x^4 y^6$

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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.

		$(6 x y^{4}) (- 2 x^{3} y^{2})$ $(6xy^4)(-2x^3 y^2)$
	$=$ $=$	$(6 \times (- 2)) \times (m \times x^{3}) \times (y^{4} \times y^{2})$ $(6 xx (-2)) xx (m xx x^3) xx (y^4 xx y^2)$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{6}^1 \times (\color{#00880A}{-2})^1 \times \color{#9a00c7}{x}^1 \times \color{#9a00c7}{x}^3 \times \color{#e65021}{y}^4 \times \color{#e65021}{y}^2$	$=$ $=$	$\color{#00880A}{-12} \times \color{#9a00c7}{x}^{1+3} \times \color{#e65021}{y}^{4+2}$
	$=$ $=$	$- 12 x^{4} y^{6}$ $-12x^4 y^6$

- 12 x^{4} y^{6}

$-12x^4 y^6$

Question 3 of 3

Simplify

(7 a^{3}) (- 3 a^{3} b^{2}) (\frac{2}{7} a b^{5})

$(7a^3)(-3a^3 b^2)(2/7ab^5)$

1. $\frac{6}{7} a b^{7}$ $6/7ab^7$
2. $- \frac{6}{7} a^{10} b$ $-6/7a^10b$
3. $6 a^{6} b^{5}$ $6a^6 b^5$
4. $- 6 a^{7} b^{7}$ $-6a^7 b^7$

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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.

		$(7 a^{3}) (- 3 a^{3} b^{2}) (\frac{2}{7} a b^{5})$ $(7a^3)(-3a^3 b^2)(2/7ab^5)$

	$=$ $=$	$(7 \times (- 3) \times \frac{2}{7}) \times (a^{3} \times a^{3} \times a) \times (b^{2} \times b^{5})$ $(7 xx (-3) xx 2/7) xx (a^3 xx a^3 xx a) xx (b^2 xx b^5)$

Using the Product of Powers, bring similar bases together.

$\color{#00880A}{7}^1 \times (\color{#00880A}{-3})^1 \times \left(\color{#00880A}{\frac{2}{7}}\right)^1 \times \color{#9a00c7}{a}^3 \times \color{#9a00c7}{a}^3 \times \color{#9a00c7}{a}^1 \times \color{#e65021}{b}^2 \times \color{#e65021}{b}^5$	$=$ $=$	$\color{#00880A}{-3 \times 2} \times \color{#9a00c7}{a}^{3+3+1} \times \color{#e65021}{b}^{2+5}$	$7 \times \frac{1}{7}$ $7 xx 1/7$ cancels out

	$=$ $=$	$- 6 a^{7} b^{7}$ $-6a^7 b^7$

- 6 a^{7} b^{7}

$-6a^7 b^7$

Multiply Exponents (Product Rule) 4

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Quiz summary

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1. Question

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Fantastic!

Product of Powers

2. Question

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Excellent!

Product of Powers

3. Question

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Keep Going!

Product of Powers

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