Mixed Operations with Indices 1
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`(8b^3)^2 b^5`Hint
Help VideoCorrect
Great Work!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, apply the power of a power to all terms inside the brackets, then simplify.$${(8b^{\color{#007DDC}{3}})}^{\color{#9a00c7}{2}} b^5$$ `=` $$(8^{\color{#9a00c7}{2}}b^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}) b^{5}$$ `=` `64b^6 b^5` Simplify further by applying the Product of Powers to the values with the same base.$$64\color{#00880A}{b}^6 \color{#00880A}{b}^5$$ `=` $$64\color{#00880A}{b}^{6+5}$$ `=` `64b^(11)` `64b^(11)` -
Question 2 of 5
2. Question
Simplify`(3m^3)^2xx m^4 xx z^0`Hint
Help VideoCorrect
Fantastic!
Incorrect
Power of Zero
$$\color{#A57200}{a^0} =\color{#A57200}{1}$$Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$First, apply the Power of Zero to the third term.`(3m^3)^2xx m^4 xx` `z^0` `=` `(3m^3)^2xx m^4 xx` `1` `=` `(3m^3)^2xx m^4` Next, apply the power of a power to the first term.$${(3m^{\color{#007DDC}{3}})}^{\color{#9a00c7}{2}} \times m^4$$ `=` $$(3^{\color{#9a00c7}{2}}m^{\color{#007DDC}{3} \times \color{#9a00c7}{2}}) \times m^{4}$$ `=` `9m^6 xx m^4` Simplify further by applying the Product of Powers to the values with the same base.$$9\color{#00880A}{m}^6 \times \color{#00880A}{m}^4$$ `=` $$9\color{#00880A}{m}^{6+4}$$ `=` `9m^10` `9m^10` -
Question 3 of 5
3. Question
Simplify`(-5a^2 b)^3 (4a^3 b^5)^2`Hint
Help VideoCorrect
Good job!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Product of Powers
$${\color{#00880A}{a}^m}\times{\color{#00880A}{a}^n}=\color{#00880A}{a}^{m+n}$$Apply the power of a power to the first bracket.$${(-5a^{\color{#007DDC}{2}} b)}^{\color{#9a00c7}{3}} {(4a^3 b^5)}^2$$ `=` $$(-5^{\color{#9a00c7}{3}}a^{\color{#007DDC}{2} \times \color{#9a00c7}{3}} b^{\color{#9a00c7}{3}}) {(4a^3 b^5)}^2$$ `=` `(-125a^6 b^3) (4a^3 b^5)^2` Do the same to the second bracket.$$(-125a^6 b^3) {(4a^\color{#007DDC}{3} b^\color{#007DDC}{5})}^\color{#9a00c7}{2}$$ `=` $$(-125a^6 b^3) (4^{\color{#9a00c7}{2}}a^{\color{#007DDC}{3} \times \color{#9a00c7}{2}} b^{\color{#007DDC}{5} \times \color{#9a00c7}{2}})$$ `=` `(-125a^6 b^3) (16a^6 b^10)` Simplify further by applying the Product of Powers to the values with the same base.$$(-125\color{#00880A}{a}^6 b^3) (16\color{#00880A}{a}^6 b^{10})$$ `=` $$- 125 \times 16 \times \color{#00880A}{a}^{6+6} \times b^3 \times b^{10}$$ Collect like terms `=` $$-2000 \times a^{12} \times \color{#00880A}{b}^3 \times \color{#00880A}{b}^{10}$$ Evaluate the constant `=` $$-2000 \times a^{12} \times \color{#00880A}{b}^{3+10}$$ `=` $$-2000 \times a^{12} \times b^{13}$$ `=` `-2000a^12 b^13` `-2000a^12 b^13` -
Question 4 of 5
4. Question
Simplify`(3x^3 y^(-2))/(-6xy^(-5))`Hint
Help VideoCorrect
Great Work!
Incorrect
Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$First, collect like terms.`(3x^3 y^(-2))/(-6xy^(-5))` `=` `(3/(-6))((x^3)/(x))((y^(-2))/(y^(-5)))` Use Quotient of Powers to simplify the fractions.$$\left(\frac{3}{-6}\right) \left(\frac{\color{#00880A}{x}^3}{\color{#00880A}{x}}\right) \left(\frac{y^{-2}}{y^{-5}}\right)$$ `=` $$-\frac{1}{2} \left(\color{#00880A}{x}^{3-1}\right) \left(\frac{y^{-2}}{y^{-5}}\right)$$ Simplify the fraction `=` $$-\frac{1}{2} x^2 \left(\frac{\color{#00880A}{y}^{-2}}{\color{#00880A}{y}^{-5}}\right)$$ `=` $$-\frac{1}{2} x^2 \color{#00880A}{y}^{-2-(-5)}$$ `=` `-1/2 x^2 y^3` `-1/2 x^2 y^3` -
Question 5 of 5
5. Question
Simplify`((x^2)/y)^5 xx 1/(2x^2)`Hint
Help VideoCorrect
Exceptional!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$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, apply the power of 5 to the top and bottom of the fraction.`((x^2)/y)^5 xx 1/(2x^2)` `=` `((x^2)^5)/(y^5) xx 1/(2x^2)` Next, apply the power of a power to the numerator of the first term.$$\frac{{(x^\color{#007DDC}{2})}^\color{#9a00c7}{5}}{y^5} \times \frac{1}{2x^2}$$ `=` $$\frac{x^{\color{#007DDC}{2} \times \color{#9a00c7}{5}}}{y^5} \times \frac{1}{2x^2}$$ `=` `(x^10)/(y^5) xx 1/(2x^2)` Bring `x` terms together in one fraction.`(x^10)/(y^5) xx 1/(2x^2)` `=` `(x^10)/(x^2) xx 1/(2y^5)` Simplify further by applying the Quotient of Powers to the values with the same base.$$\frac{\color{#00880A}{x}^{10}}{\color{#00880A}{x}^2} \times \frac{1}{2y^5}$$ `=` $$\frac{\color{#00880A}{x}^{10-2}}{1} \times \frac{1}{2y^5}$$ `=` `(x^8)/(2y^5)` `(x^8)/(2y^5)`
Quizzes
- Index Notation 1
- Index Notation 2
- Index Notation 3
- Multiply Indices 1
- Multiply Indices 2
- Multiply Indices 3
- Multiply Indices 4
- Divide Indices 1
- Divide Indices 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 Indices 1
- Negative Indices 2
- Negative Indices 3
- Fractional Indices 1
- Fractional Indices 2
- Fractional Indices 3
- Mixed Operations with Indices 1
- Mixed Operations with Indices 2