Question 1

"Which of the following correctly simplifies $$(-4)^6$$?"

Accepted Answer

$$4096$$

Question 2

"What is the value of $$1^{2024}$$?"

Accepted Answer

$$1$$

Question 3

"Simplify the expression $$x^5$$ 	imes $$x^3$$ using the product rule for exponents."

Accepted Answer

$$x^{8}$$

Question 4

"Evaluate $$(-2)^5$$."

Accepted Answer

$$-32$$

Question 5

"Which rule is used to simplify $$a^m 	imes a^n$$?"

Accepted Answer

Add the exponents

Question 6

"Simplify the expression $$y^{12}$$ / $$y^7$$."

Accepted Answer

$$y^{5}$$

Question 7

"What is the value of $$a^0$$ for any $$a \neq 0$$?"

Accepted Answer

$$1$$

Question 8

"If $$b^{-4} is $$written with a positive exponent, what is the equivalent expression?"

Accepted Answer

$$1/b^4$$

Question 9

"Simplify the following: $$3^4$$ / $$3^2$$."

Accepted Answer

$$3^2$$

Question 10

"A scientist measures the intensity of a signal as $$I = 2$$^{-3}$$. What is the value of I$?"

Accepted Answer

$$1/8$$

Question 11

"Which of the following is true for $$(-a)^{	ext{even}$$}$$?"

Accepted Answer

$$(-a)^{	ext{even}$$} = $$a^{	ext{even}$$}$$

Question 12

"A medication's concentration decreases according to $$C = 5 	imes 0.5^t. $$What is $$C$$ when $$t = 3$$?"

Accepted Answer

$$0.625$$

Question 13

"Simplify $$(-5)^4$$."

Accepted Answer

$$625$$

Question 14

"Which of the following is the correct application of the quotient rule for exponents?"

Accepted Answer

$$a^m / a^n = a$$^{m-n}$$

Question 15

"If $$x^{-2}$$ = $$1/x^2$$, what is $$x^{-2}$$ 	imes $$x^5$$?"

Accepted Answer

$$x^3$$

Question 16

"A population doubles every year. If the initial population is $$P_0$$, what is the population after $$n$$ years?"

Accepted Answer

$$P_0$$ 	imes 2^n$$

Question 17

"Simplify $$2^3$$ 	imes $$2^{-5}$$."

Accepted Answer

$$2^{-2}$$

Question 18

"Which of the following is equivalent to $$1/a^{-n}$$?"

Accepted Answer

$$a^n$$

Question 19

"A radioactive substance decays according to $$N = N_0$ 	imes (1/2)^t. $$What is $$N$$ after $$t = 4 if$$ $$N_0 = 80$?"

Accepted Answer

$$10$$

Question 20

"Simplify $$(-7)^3$$."

Accepted Answer

$$-343$$

Rules of Exponents: Essential Properties and Applications

Study Guide - Practice Questions