Mixed Operations with Indices 2
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`(2x^(2/3))^3xx(9x^4)^(1/2)`Hint
Help VideoCorrect
Correct!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$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.$$(2x^{\color{#007DDC}{\frac{2}{3}}})^{\color{#9a00c7}{3}} \times (9x^{\color{#007DDC}{4}})^{\color{#9a00c7}{\frac{1}{2}}}$$ `=` $$(2^{\color{#9a00c7}{3}}\times x^{\color{#007DDC}{\frac{2}{3}} \times \color{#9a00c7}{3}})\times(9^{\color{#9a00c7}{\frac{1}{2}}}\times x^{\color{#007DDC}{4} \times \color{#9a00c7}{\frac{1}{2}}})$$ `=` `8x^2xx9^(1/2)xx x^2` `2/3xx3=2` and `4xx1/2=2` Next, use Fractional Powers to simplify the expression further.$$8x^2 \times 9^{\frac{\color{#004ec4}{1}}{\color{#D800AD}{2}}} \times x^2$$ `=` $$8x^2 \times (\sqrt[\color{#D800AD}{2}]{9})^{\color{#004ec4}{1}} \times x^2$$ `=` `8x^2xx(3)^1xxx^2` `root (2)(9)=3` `=` `8x^2xxx^2xx3` Rearrange the values Finally, simplify further by applying the Product of Powers to the values with the same base.$$8\color{#00880A}{x}^2\times \color{#00880A}{x}^2 \times 3$$ `=` $$8 \times 3 \times \color{#00880A}{x}^{2+2}$$ `=` `24x^4` `24x^4` -
Question 2 of 5
2. Question
Simplify`((x^4)/(y^3))^3 xx 4/(7x^5)`Hint
Help VideoCorrect
Great Work!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$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 3 to the top and bottom of the fraction.`((x^4)/(y^3))^3 xx 4/(7x^5)` `=` `((x^4)^3)/((y^3)^3) xx 4/(7x^5)` Next, apply the power of a power to the first term.$$\frac{{(x^\color{#007DDC}{4})}^\color{#9a00c7}{3}}{{(y^\color{#007DDC}{3})}^\color{#9a00c7}{3}} \times \frac{4}{7x^5}$$ `=` $$\frac{x^{\color{#007DDC}{4} \times \color{#9a00c7}{3}}}{y^{\color{#007DDC}{3} \times \color{#9a00c7}{3}}} \times \frac{4}{7x^5}$$ `=` `(x^12)/(y^9) xx 4/(7x^5)` Bring `x` terms together in one fraction.`(x^12)/(y^9) xx 4/(7x^5)` `=` `(x^12)/(x^5) xx 4/(7y^9)` Simplify further by applying the Quotient of Powers to the values with the same base.$$\frac{\color{#00880A}{x}^{12}}{\color{#00880A}{x}^5} \times \frac{4}{7y^9}$$ `=` $$\frac{\color{#00880A}{x}^{12-5}}{1} \times \frac{4}{7y^9}$$ `=` `(4x^7)/(7y^9)` `(4x^7)/(7y^9)` -
Question 3 of 5
3. Question
Simplify`(4x^(1/4))^2 -: (64x^3)^(1/3)`Hint
Help VideoCorrect
Excellent!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Quotient of Powers
$${\color{#00880A}{a}^m}\div{\color{#00880A}{a}^n}=\frac{{\color{#00880A}{a}^m}}{{\color{#00880A}{a}^n}}=\color{#00880A}{a}^{m-n}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$First, apply the power of a power to all terms inside the brackets, then simplify.$${(4x^{\color{#007DDC}{\frac{1}{4}}})}^\color{#9a00c7}{2} \div {(64x^\color{#007DDC}{3})}^{\color{#9a00c7}{\frac{1}{3}}}$$ `=` $$\left(4^\color{#9a00c7}{2} \times x^{\color{#007DDC}{\frac{1}{4}} \times \color{#9a00c7}{2}} \right) \div \left(64^{\color{#9a00c7}{\frac{1}{3}}} \times x^{\color{#007DDC}{3} \times \color{#9a00c7}{\frac{1}{3}}} \right)$$ `=` `(16 \times x^(1/2)) -: (4 \times x^1)` `1/4xx2=1/2` and `3xx1/3=1` `=` `(16x^(1/2))/(4x^1)` `=` `(4x^(1/2))/(x^1)` `16-:4=4` Simplify further by applying the Quotient of Powers.$$\frac{4\color{#00880A}{x}^\frac{1}{2}}{\color{#00880A}{x}^1}$$ `=` $$4\color{#00880A}{x}^{\frac{1}{2}-1}$$ `=` `4x^(-1/2)` Finally, simplify further by applying Negative Powers.$$4x^{-\color{#e65021}{\frac{1}{2}}}$$ `=` $$\frac{4}{x^\color{#e65021}{\frac{1}{2}}}$$ `=` `4/(sqrtx)` `4/(sqrtx)` -
Question 4 of 5
4. Question
Simplify`(a^2)^(-3/2) -: (b^(-1/2))^3`Hint
Help VideoCorrect
Good job!
Incorrect
Power of a Power
$${(a^\color{#007DDC}{m})}^{\color{#9a00c7}{n}}=a^{\color{#007DDC}{m} \times \color{#9a00c7}{n}}$$Negative Powers
$$a^{-\color{#e65021}{n}}=\frac{1}{a^\color{#e65021}{n}}$$Fractional Powers
$$a^{\frac{\color{#004ec4}{T}}{\color{#D800AD}{B}}}=(\sqrt[\color{#D800AD}{B}]{a})^{\color{#004ec4}{T}}$$First, apply the power of a power to all terms inside the brackets, then simplify.$${(a^\color{#007DDC}{2})}^\color{#9a00c7}{-\frac{3}{2}} \div {(b^\color{#007DDC}{-\frac{1}{2}})}^\color{#9a00c7}{3}$$ `=` $$\left(a^{\color{#007DDC}{2} \times \left(\color{#9a00c7}{-\frac{3}{2}}\right)}\right) \div \left(b^{\color{#007DDC}{-\frac{1}{2}} \times \color{#9a00c7}{3}}\right)$$ `=` `a^(-3) -: b^(-3/2)` Simplify further by applying Negative Powers.$$a^{-\color{#e65021}{3}} \div b^{-\color{#e65021}{\frac{3}{2}}}$$ `=` $$\frac{1}{a^\color{#e65021}{3}} \div \frac{1}{b^\color{#e65021}{\frac{3}{2}}}$$ Finally, apply Fractional Powers and simplify.$$\frac{1}{a^3} \div \frac{1}{b^\frac{\color{#004ec4}{3}}{\color{#D800AD}{2}}}$$ `=` $$\frac{1}{a^3} \div \frac{1}{\left(\sqrt[\color{#D800AD}{2}]{b}\right)^\color{#004ec4}{3}}$$ `=` $$\frac{1}{a^3} \div \frac{1}{\sqrt{b^3}}$$ `=` $$\frac{1}{a^3} \times \frac{\sqrt{b^3}}{1}$$ `=` `(sqrt(b^3))/(a^3)` `(sqrt(b^3))/(a^3)` -
Question 5 of 5
5. Question
Simplify`(1/3 ab^3)^2 [(-3b)^2]^3`Hint
Help VideoCorrect
Correct!
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 each term in the brackets.$${\left(\frac{1}{3} ab^\color{#007DDC}{3} \right)}^\color{#9a00c7}{2} \left[{(-3b)}^\color{#007DDC}{2}\right]^\color{#9a00c7}{3}$$ `=` $$\left(\frac{1}{3}\right)^\color{#9a00c7}{2} \times a^\color{#9a00c7}{2} \times b^{\color{#007DDC}{3} \times \color{#9a00c7}{2}} \times {(-3b)}^{\color{#007DDC}{2} \times \color{#9a00c7}{3}}$$ `=` `1/9 a^2 b^6 xx (-3b)^6` `=` `1/9 a^2 b^6 xx (-3)^6 b^6` `=` `((-3)^6)/9 a^2 b^6 b^6` `=` `729/9 a^2 b^6 b^6` `=` `81a^2 b^6 b^6` Simplify further by applying the Product of Powers to the values with the same base.$$81a^2 \color{#00880A}{b}^6 \color{#00880A}{b}^6$$ `=` $$81a^2 \color{#00880A}{b}^{6+6}$$ `=` `81a^2 b^12` `81a^2 b^12`
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