Question 1

Which of the following correctly expresses $$a^{-n}$$, where $$a is a $$nonzero real number and $$n is a $$positive integer?

Accepted Answer

$$a^{-n}$$ = \dfrac{1}{a^n}$$

Question 2

Simplify the expression $$\dfrac{2^5$ \cdot 2$$^{-3}$$}{2^2$}.$$

Accepted Answer

$$2^2$$

Question 3

Which property allows you to write $$\dfrac{a^m}{a^n} = a$$^{m-n}$$ for any nonzero real number a$ and integers m$$, n$$?

Accepted Answer

Quotient of Powers Property

Question 4

Evaluate $$\left(\dfrac{3^4$}{3^2$}\$$right)^3$$.

Accepted Answer

$$3^9$$

Question 5

Which of the following is equivalent to $$\dfrac{5$$^{-3}$$}{5$$^{-7}$$}$$?

Accepted Answer

$$5^{4}$$

Question 6

A scientist is working with a chemical solution where the concentration is halved every hour. If the initial concentration is $$C_0$$, which expression represents the concentration after $$n$$ hours?

Accepted Answer

$$C_0$$ \cdot \dfrac{1}{2^n}$$

Question 7

Simplify $$\left(\dfrac{x^3$ y$$^{-2}$$}{x$$^{-1}$$ y^4$}\$$right)^2$$.

Accepted Answer

$$x^8$$ $$y^{-12}$$

Question 8

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

Accepted Answer

$$a^{12}$$ $$b^{-10}$$

Question 9

If $$a$$ and $$b$$ are nonzero real numbers, which of the following is equivalent to $$\left(\dfrac{a}{b}\$$right)^{-n}$$?

Accepted Answer

$$\dfrac{b^n}{a^n}$$

Question 10

A medication's effectiveness decreases by a factor of $$\dfrac{1}{3}$$ every hour. If the initial effectiveness is $$E_0$$, what is the effectiveness after $$t$$ hours?

Accepted Answer

$$E_0$$ \cdot \dfrac{1}{3^t}$$

Question 11

Which of the following is the correct simplification of $$\dfrac{(2x$$^{-3}$$y^2)^2$}{(x^2$y^{-1})^3$}$$?

Accepted Answer

$$\dfrac{4x$$^{-6}$$y^4$$}{$$x^6y$$^{-3}$$} = 4x$$^{-12}$$y^7$

Question 12

Which of the following is the correct application of the power of a quotient property?

Accepted Answer

$$\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$$

Question 13

Simplify $$\left(\dfrac{2^3$}{4^2$}\$$right)^{-1}$$.

Accepted Answer

$$2^1$$

Question 14

Which of the following is equivalent to $$x^{-2}y^3$?

Accepted Answer

$$\dfrac{y^3$}{x^2$}$$

Question 15

If $$a = 2$$ and $$b = 3$$, evaluate $$\left(\dfrac{a^2$}{b$$^{-1}$$}\$$right)^{-2}$$.

Accepted Answer

$$\dfrac{1}{1296}$$

Integer Exponents and Scientific Notation

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