Question 1

Which of the following correctly expresses $$a^{-3}$$ for any nonzero real number $$a$$?

Accepted Answer

$$a^{-3}$$ = \dfrac{1}{$$a^3$$}$$

Question 2

If $$b is a $$nonzero real number, what is the value of $$b^0$$?

Accepted Answer

$$b^0 = 1$

Question 3

Which of the following is undefined?

Accepted Answer

$$0^0$$

Question 4

Simplify the expression $$\left(\dfrac{2}{3}\$$right)^{-2}$$.

Accepted Answer

$$\dfrac{9}{4}$$

Question 5

Which property of exponents justifies the equality $$a^m \cdot a^n = a$$^{m+n}$$?

Accepted Answer

Product of powers property

Question 6

A biologist is studying bacteria growth. If the number of bacteria doubles every hour, and there are initially $$N_0$$ bacteria, which expression gives the number of bacteria after $$t$$ hours?

Accepted Answer

$$N_0$$ \cdot 2^t$$

Question 7

Simplify the expression $$\dfrac{a^5$}{a^2$}$$ for $$a 
eq 0.$$

Accepted Answer

$$a^3$$

Question 8

Which of the following is equivalent to $$\$$left(a^2$$\$$right)^3$$?

Accepted Answer

$$a^6$$

Question 9

A medication's concentration in the bloodstream halves every 4 hours. If the initial concentration is $$C_0$$, what is the concentration after 12 hours?

Accepted Answer

$$C_0$$ \cdot \left(\dfrac{1}{2}\$$right)^3$$

Question 10

Simplify the expression $$\left(\dfrac{a^3$}{b^2$}\$$right)^{-2}$$ for a$$, b 
eq 0$$.

Accepted Answer

$$\dfrac{b^4$}{a^6$}$$

Question 11

Which of the following correctly applies the property $$(ab)^n = a^n b^n to$$ $$(3x)^4$$?

Accepted Answer

$$3^4$$ $$x^4$$

Question 12

If $$a$$ and $$b$$ are nonzero real numbers, which of the following is equivalent to $$\left(\dfrac{a}{b}\$$right)^{-3}$$?

Accepted Answer

$$\dfrac{b^3$}{a^3$}$$

Question 13

A radioactive substance decays so that its mass halves every day. If the initial mass is $$M_0$$, what is the mass after $$n$$ days?

Accepted Answer

$$M_0$$ \cdot \left(\dfrac{1}{2}\right)^n$$

Question 14

Simplify the expression $$a^0$$ $$b^0$$ for $$a, b 
eq 0.$$

Accepted Answer

$$1$$

Question 15

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

Accepted Answer

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

Question 16

If $$a = 2$$ and $$n = -3$$, what is the value of $$a^n$$?

Accepted Answer

$$\dfrac{1}{8}$$

Question 17

Which of the following is equivalent to $$\$$left(a^{-2}$$\$$right)^3$$?

Accepted Answer

$$a^{-6}$$

Question 18

A population of insects triples every week. If the initial population is $$P_0$$, what is the population after $$4$$ weeks?

Accepted Answer

$$P_0$$ \cdot $$3^4$$

Question 19

Simplify the expression $$\dfrac{2$$^{-3}$$}{4$$^{-2}$$}.$$

Accepted Answer

$$4$$

Integer Exponents: Definitions, Properties, and Examples

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