Question 1

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

Accepted Answer

$$81$$

Question 2

What is the simplified form of $$a^5$$ 	imes $$a^3$$?

Accepted Answer

$$a^8$$

Question 3

Evaluate $$\frac{2^7$}{2^3$}.$$

Accepted Answer

$$2^4$$

Question 4

Which of the following statements is true for any nonzero number $$a$$?

Accepted Answer

$$a^0 = 1$

Question 5

Simplify $$\left( -2 \$$right)^3$$.

Accepted Answer

$$-8$$

Question 6

If $$x^{-4} is $$written with a positive exponent, which of the following is correct?

Accepted Answer

$$\frac{1}{x^4$}$$

Question 7

A scientist is calculating the concentration of a substance and writes $$y^{30}$$ 	imes $$y^{70}. $$What is the simplified form?

Accepted Answer

$$y^{100}$$

Question 8

Which of the following correctly applies the quotient rule to $$\frac{a^7$}{a^2$}$$?

Accepted Answer

$$a^5$$

Question 9

What is the value of $$1^{1000}$$?

Accepted Answer

$$1$$

Question 10

Simplify $$\frac{3$$^{-2}$$}{3$$^{-5}$$}.$$

Accepted Answer

$$3^{3}$$

Question 11

A medical researcher is diluting a solution and needs to calculate $$\left( \frac{1}{2} \$$right)^{-3}$$. What is the result?

Accepted Answer

$$8$$

Question 12

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

Accepted Answer

$$a^n$$

Question 13

If $$(-5)^{2} is $$calculated, what is the result?

Accepted Answer

$$25$$

Question 14

Simplify the expression $$\frac{4^3$}{4^1$}.$$

Accepted Answer

$$4^2$$

Question 15

A biologist is modeling population growth and uses the expression $$b^0. $$What does this equal for any nonzero $$b$$?

Accepted Answer

$$1$$

Question 16

Which of the following is the correct simplification of $$2^2$$ 	imes $$2^5$$?

Accepted Answer

$$2^{7}$$

Question 17

Simplify $$\left( -4 \$$right)^2$$.

Accepted Answer

$$16$$

Question 18

Which of the following is the correct application of the negative exponent rule for $$a^{-3}$$?

Accepted Answer

$$\frac{1}{a^3$}$$

Question 19

A chemist writes $$\frac{5^0$}{2^0$}. $$What is the value?

Accepted Answer

$$1$$

Question 20

Which of the following is the correct simplification of $$\frac{2^4$}{2^4$}$$?

Accepted Answer

$$2^0$$

Rules of Exponents: Essential Properties and Applications

Study Guide - Practice Questions