Topics
>
Algebra 2>
Exponents>
Divide Exponents (Quotient Rule)>
Divide Exponents (Quotient Rule) 2Divide Exponents (Quotient Rule) 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
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:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
Question 1 of 4
1. Question
Simplify`(3^(-5))/(3^(-2))`Write fractions as “a/b”- (1/27)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Using the Quotient of Powers, bring similar bases together.$$\frac{\color{#00880A}{3}^{-5}}{\color{#00880A}{3}^{-2}}$$ `=` $$\color{#00880A}{3}^{(-5)-(-2)}$$ `=` $$\color{#00880A}{3}^{(-5)+2}$$ `=` `3^(-3)` Use Negative Powers to further simplify the expression.$$3^{\color{#e65021}{-3}}$$ `=` $$\frac{1}{3^{\color{#e65021}{3}}}$$ `=` `1/(27)` `3 xx 3 xx 3 = 27` `1/(27)` -
Question 2 of 4
2. Question
Simplify`7a^6 b^2 -: 4ab^2`Hint
Help VideoCorrect
Excellent!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Power of Zero
Anything to the power of zero becomes `1`.First, bring the like terms together`7a^6 b^2 -: 4ab^2` `=` `(7/4)xx((a^6)/a)xx((b^2)/(b^2))` Using the Quotient of Powers, bring similar bases together.$$\frac{7}{4} \times \frac{\color{#00880A}{a}^6}{\color{#00880A}{a}^1} \times \frac{\color{#9a00c7}{b}^2}{\color{#9a00c7}{b}^2}$$ `=` $$\frac{7}{4} \times \color{#00880A}{a}^{6-1} \times \color{#9a00c7}{b}^{2-2}$$ `=` $$\frac{7}{4} \times \color{#00880A}{a}^5 \times \color{#9a00c7}{b}^0$$ `=` `7/4 xx a^5 xx 1` `b^0=1` `=` `(7a^5)/4` `(7a^5)/4` -
Question 3 of 4
3. Question
Simplify`(14m^2y)/(2my^2)`Write fractions as “a/b”- (7m/y)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$First, bring the like terms together`(14m^2y)/(2my^2)` `=` `(14/2)xx((m^2)/m)xx((y)/(y^2))` Using the Quotient of Powers, bring similar bases together.$$\frac{14}{2} \times \frac{\color{#00880A}{m}^2}{\color{#00880A}{m}^1} \times \frac{\color{#9a00c7}{y}^1}{\color{#9a00c7}{y}^2}$$ `=` $$7 \times \color{#00880A}{m}^{2-1} \times \color{#9a00c7}{y}^{1-2}$$ `=` `7my^(-1)` Use Negative Powers to further simplify the expression.$$7my^{\color{#e65021}{-1}}$$ `=` $$\frac{7m}{y^{\color{#e65021}{1}}}$$ `=` `(7m)/y` A power of `1` does not need to be written `(7m)/y` -
Question 4 of 4
4. Question
If `A=21x^5 y^3`, find the width of this rectangle:
Hint
Help VideoCorrect
Well done!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Area of a Rectangle
`A=L xx W`Since we are looking for the Width, we can take the Area formula and make Width (`W`) the subject.`A` `=` `LxxW` `A``-:L` `=` `LxxW``-:L` Divide both sides by `L` `A/L` `=` `W` `W` `=` `A/L` Substitute the known values.`A=21x^5 y^3``L=7x^3 y^2``W` `=` `A/L` `=` `(21x^5 y^3)/(7x^3 y^2)` `=` `21/7 xx (x^5)/(x^3) xx (y^3)/(y^2)` Join similar terms `=` $$3 \times \frac{\color{#00880A}{x}^5}{\color{#00880A}{x}^3} \times \frac{\color{#9a00c7}{y}^3}{\color{#9a00c7}{y}^2}$$ Simplify using Quotient of Powers `=` $$3\color{#00880A}{x}^{(5-3)}\color{#9a00c7}{y}^{(3-2)}$$ `=` `3x^2 y` `3x^2 y`
Quizzes
- Exponent Notation 1
- Exponent Notation 2
- Exponent Notation 3
- Multiply Exponents (Product Rule) 1
- Multiply Exponents (Product Rule) 2
- Multiply Exponents (Product Rule) 3
- Multiply Exponents (Product Rule) 4
- Divide Exponents (Quotient Rule) 1
- Divide Exponents (Quotient Rule) 2
- Powers of a Power 1
- Powers of a Power 2
- Powers of a Power 3
- Powers of a Power 4
- Zero Powers 1
- Zero Powers 2
- Negative Exponents 1
- Negative Exponents 2
- Negative Exponents 3
- Rational Exponents 1
- Rational Exponents 2
- Rational Exponents 3
- Mixed Operations with Exponents 1
- Mixed Operations with Exponents 2