Question 1

Which of the following correctly applies the power of a quotient rule to $$\left( \dfrac{a^3$}{b^2$} \$$right)^4$$?

Accepted Answer

$$\dfrac{a$$^{12}$$}{b^8$}$$

Question 2

Simplify the expression $$\dfrac{2^5$ \cdot 2$$^{-3}$$}{2^2$}$$ and write your answer with a positive exponent.

Accepted Answer

$$2^{0} = 1$

Question 3

Which of the following is equivalent to $$x^{-3}y^4$ with only positive exponents?

Accepted Answer

$$\dfrac{y^4$}{x^3$}$$

Question 4

If $$a^x \cdot a^y = a$$^{12}$$ and x = 7$, what is the value of y$?

Accepted Answer

$$5$$

Question 5

Which property of exponents justifies the step from $$b^6$$ \div $$b^2 to$$ $$b^{4}$$?

Accepted Answer

Quotient Rule: $$\dfrac{b^m}{b^n} = b$$^{m-n}$$

Question 6

Simplify $$\left( 3x^2$y^{-1}$$ \$$right)^3$ and write your answer with positive exponents.

Accepted Answer

$$27x^6/y^3$

Question 7

Which of the following is equivalent to $$\dfrac{5x$$^{-2}$$y^3$$}{$$10x^4y$$^{-1}$$}$$ with positive exponents?

Accepted Answer

$$\dfrac{y^4$}{2x^6$}$$

Question 8

Solve for $$x$$: $$7^{x-1} = 49$.

Accepted Answer

$$x = 3$$

Question 9

Which of the following best describes the meaning of a zero exponent, such as $$a^0 ($$where $$a 
eq 0$$)?

Accepted Answer

$$a^0 = 1$

Question 10

Simplify $$\left( \dfrac{2x$$^{-2}$$}{y^3$} \$$right)^{-2}$$ and write your answer with positive exponents.

Accepted Answer

$$\dfrac{y^6$}{4x^4$}$$

Question 11

Which of the following is the correct simplification of $$\sqrt[3]{x^6$}$$?

Accepted Answer

$$x^2$$

Question 12

If $$b^{-4}$$ = \dfrac{1}{$$b^4$$}$$, which property of exponents is being used?

Accepted Answer

Negative Exponent Rule

Question 13

Simplify $$\left( x^2$y^{-3}$$ \$$right)^4$ and write your answer with positive exponents.

Accepted Answer

$$\dfrac{x^8$}{y$$^{12}$$}$$

Question 14

Which of the following is equivalent to $$\dfrac{a^5$b^{-2}$$}{$$a^{-3}b^4$}$$ with positive exponents?

Accepted Answer

$$\dfrac{a^8$}{b^6$}$$

Question 15

A scientist is diluting a solution by a factor of $$10$$ each time. If the initial concentration is $$C_0$$, what is the concentration after $$n$$ dilutions?

Accepted Answer

$$C_0$$ \cdot $$10^{-n}$$

Question 16

Simplify $$\dfrac{(2x^3$y^{-2})^2$}{4x$$^{-1}$$y}$$ and write your answer with positive exponents.

Accepted Answer

$$x^7/y^5$

Question 17

Which of the following is the correct simplification of $$\left( \dfrac{a^2$b^{-3}$$}{$$c^4$$} \$$right)^3$?

Accepted Answer

$$\dfrac{a^6$}{b^9$c^{12}$$}$

Question 18

If $$x^{1/2} = 9$, what is the value of x$?

Accepted Answer

$$81$$

Question 19

Which of the following is equivalent to $$\sqrt[4]{x^8$y^{12}$$}$?

Accepted Answer

$$x^2y^3$

C1

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