Multiply Exponents (Product Rule) 4

Quiz summary

0 of 3 questions completed

Questions:

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

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

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Fantastic!

Product of Powers

2. Question

Hint

Excellent!

Product of Powers

3. Question

Hint

Keep Going!

Product of Powers

Quizzes