Negative Exponents 3
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
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
- 5
- Answered
- Review
-
Question 1 of 5
1. Question
Simplify`[(-a^2)/(b^3)]^(-5)`Hint
Help VideoCorrect
Keep Going!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$A negative power means we flip a fraction and make the power positive.`[(-a^2)/(b^3)]^(-5)` `=` $$\left[\frac{b^{\color{#007DDC}{3}}}{-a^{\color{#007DDC}{3}}}\right]^\color{#9a00c7}{5}$$ `=` $$\frac{b^{\color{#007DDC}{3} \times \color{#9a00c7}{5}}}{-a^{\color{#007DDC}{2} \times \color{#9a00c7}{5}}}$$ `=` `(b^(15))/(-a^(10))` `(b^(15))/(-a^(10))` -
Question 2 of 5
2. Question
Simplify`(m^(-3) n^5)/(z^(-4))`Hint
Help VideoCorrect
Excellent!
Incorrect
Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$$$\frac{1}{a^{-\color{#e65021}{n}}}=a^\color{#e65021}{n}$$First, separate the bases..`(m^(-3) n^5)/(z^(-4))` `=` `(m^(-3))/1 xx (n^5)/1 xx 1/(z^(-4))` Now use Negative Powers to simplify the expression.$$\frac{m^{\color{#e65021}{-3}}}{1} \times \frac{n^5}{1} \times \frac{1}{z^{\color{#e65021}{-4}}}$$ `=` $$\frac{1}{m^{\color{#e65021}{3}}} \times \frac{n^5}{1} \times \frac{z^{\color{#e65021}{4}}}{1}$$ `=` `(n^5 z^4)/(m^3)` `(n^5 z^4)/(m^3)` -
Question 3 of 5
3. Question
Simplify`((10x^2 y^(-2))^3)/((2x^(-1)y^3)^2)`Hint
Help VideoCorrect
Correct!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Use Power of a Power and Negative Powers to simplify the expression.$$\frac{(10x^{\color{#007DDC}{2}}y^{\color{#007DDC}{-2}})^{\color{#9a00c7}{3}}}{(2x^{\color{#007DDC}{-1}}y^{\color{#007DDC}{3}})^{\color{#9a00c7}{2}}}$$ `=` $$\frac{10^{\color{#9a00c7}{3}}x^{\color{#007DDC}{2} \times \color{#9a00c7}{3}}y^{\color{#007DDC}{-2} \times \color{#9a00c7}{3}}}{2^{\color{#9a00c7}{2}}x^{\color{#007DDC}{-1} \times \color{#9a00c7}{2}}y^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}}$$ `=` $$\frac{1000x^6 y^{\color{#e65021}{-6}}}{4x^{\color{#e65021}{-2}}y^6}$$ `=` $$\frac{1000x^6 \times x^{\color{#e65021}{2}}}{4y^6 \times y^{\color{#e65021}{6}}}$$ Finally, use the Product of Powers to simplify the expression further.$$\frac{1000\color{#00880A}{x}^6 \times \color{#00880A}{x}^2}{4y^6 \times y^6}$$ `=` $$\frac{1000\color{#00880A}{x}^{6+2}}{4y^6 \times y^6}$$ `=` $$\frac{1000x^8}{4\color{#00880A}{y}^6 \times \color{#00880A}{y}^6}$$ `=` $$\frac{1000x^8}{4\color{#00880A}{y}^{6+6}}$$ `=` $$\frac{250x^8}{y^{12}}$$ `(1000)/4=250` `(250x^8)/(y^(12))` -
Question 4 of 5
4. Question
Simplify`(-3m^(-2))/(-4m^(-3))`Hint
Help VideoCorrect
Nice Job!
Incorrect
Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$First, separate the bases.`(-3m^(-2))/(-4m^(-3))` `=` `((-3)/(-4))((m^(-2))/(m^(-3)))` `=` `(3/4)((m^(-2))/(m^(-3)))` Recall, 
Now, use the Quotient of Powers to simplify the expression further.$$\left(\frac{3}{4}\right)\left(\frac{\color{#00880A}{m}^{-2}}{\color{#00880A}{m}^{-3}}\right)$$ `=` $$\left(\frac{3}{4}\right)\left(\color{#00880A}{m}^{-2-(-3)}\right)$$ `=` $$\left(\frac{3}{4}\right)\left(\color{#00880A}{m}^{-2+3}\right)$$ `=` `3/4m` A power of `1` does not need to be written `3/4m` -
Question 5 of 5
5. Question
Simplify`[(35x^(-2) y^4)/(7x^4 y^(-6))]^(-1)`Hint
Help VideoCorrect
Great Work!
Incorrect
Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$A negative power means we flip a fraction and make the power positive.`[(35x^(-2) y^4)/(7x^4 y^(-6))]^(-1)` `=` `[(7x^4 y^(-6))/(35x^(-2) y^4)]^1` `=` `(7x^4 y^(-6))/(35x^(-2) y^4)` A power of `1` does not need to be written `=` $$\frac{7x^4 y^{-6} \color{#CC0000}{\div7}}{35x^{-2} y^4 \color{#CC0000}{\div7}}$$ Divide the numerator and denominator by `7` `=` $$\frac{x^4 y^{-6}}{5x^{-2} y^4}$$ Now, use the Quotient of Powers to simplify the expression further.$$\frac{\color{#00880A}{x}^4 y^{-6}}{5\color{#00880A}{x}^{-2} y^4}$$ `=` $$\frac{\color{#00880A}{x}^{4-(-2)}y^{-6}}{5y^4}$$ `=` $$\frac{\color{#00880A}{x}^{4+2}y^{-6}}{5y^4}$$ `=` $$\frac{x^6\color{#00880A}{y}^{-6}}{5\color{#00880A}{y}^4}$$ `=` $$\frac{x^6\color{#00880A}{y}^{-6-4}}{5}$$ `=` $$\frac{x^6\color{#00880A}{y}^{-6+(-4)}}{5}$$ `=` $$\frac{x^6 y^{\color{#e65021}{-10}}}{5}$$ `=` $$\frac{x^6}{5y^{\color{#e65021}{10}}}$$ `(x^6)/(5y^(10))`
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