Product Rule: $$a^m \times a^n = a$$^{m+n}$$

Question 1

Which of the following is the correct value for $$(-3)^4$$?

Accepted Answer

$$81$$

Question 2

What is the result of $$a^0$$ for any nonzero real number $$a$$?

Accepted Answer

$$1$$

Question 3

Simplify the expression $$y^{30}$$ 	imes $$y^{70}$$ using exponent rules.

Accepted Answer

$$y^{100}$$

Question 4

Evaluate $$(-2)^3.$$

Accepted Answer

$$-8$$

Question 5

Which rule is used to simplify $$\dfrac{a^m}{a^n}$$?

Accepted Answer

$$a^{m-n}$$

Question 6

If $$a^{-n} is $$given, which of the following is equivalent?

Accepted Answer

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

Question 7

What is the value of $$1^{100}$$?

Accepted Answer

$$1$$

Question 8

Simplify $$\dfrac{2^4$}{2^2$}.$$

Accepted Answer

$$2^2$$

Question 9

Which of the following correctly applies the product rule to $$4^2$$ 	imes $$4^1$$?

Accepted Answer

$$4^3$$

Question 10

A scientist is calculating the concentration of a solution and needs to simplify $$\dfrac{y$$^{-3}$$}{y^5$}. $$What is the result?

Accepted Answer

$$y^{-8}$$

Question 11

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

Accepted Answer

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

Question 12

Simplify $$\dfrac{1}{a$$^{-n}$$}.$$

Accepted Answer

$$a^n$$

Question 13

A medical researcher is analyzing exponential growth and needs to compute $$2^0. $$What is the value?

Accepted Answer

$$1$$

Question 14

Which exponent rule allows you to write $$a^m 	imes a^n as a $$single power?

Accepted Answer

Product Rule: $$a^m 	imes a^n = a$$^{m+n}$$

Question 15

Simplify $$\dfrac{2^2$}{2^5$}$$ and express your answer with a positive exponent.

Accepted Answer

$$\dfrac{1}{2^3$}$$

Question 16

A chemist is working with a formula that includes $$(-4)^2. $$What is the value?

Accepted Answer

$$16$$

Question 17

Which of the following is the correct simplification for $$a^5$$ \div $$a^2$$?

Accepted Answer

$$a^3$$

Question 18

If $$a is a $$nonzero real number, what is $$\dfrac{1}{a$$^{-4}$$}$$?

Accepted Answer

$$a^4$$

Question 19

A biologist is modeling population growth and uses the expression $$3^0. $$What is the value?

Accepted Answer

$$1$$

Question 20

Which of the following is the correct simplification for $$(-5)^3$$?

Accepted Answer

$$-125$$

Rules of Exponents: Essential Properties and Applications

Study Guide - Practice Questions