$$4^3 = 4$$ \times 4 \times 4$$

Question 1

Which of the following correctly expresses $$4^3$$ using the definition of exponents?

Accepted Answer

$$4^3 = 4$$ 	imes 4 	imes 4$$

Question 2

What is the value of $$(-3)^2$$?

Accepted Answer

$$9$$

Question 3

Simplify $$x^3$$ $$y^{-2}.$$

Accepted Answer

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

Question 4

Which of the following is equivalent to $$4^{-2}$$?

Accepted Answer

$$\dfrac{1}{16}$$

Question 5

Given $$a, b, c$$ are real numbers, which exponent rule is correctly applied in $$a^b \cdot a^c$$?

Accepted Answer

$$a^{b+c}$$

Question 6

Simplify $$(4^2)^3$.

Accepted Answer

$$4^6$$

Question 7

Which of the following is equivalent to $$a^c \cdot b^c$$?

Accepted Answer

$$(a \cdot b)^c$$

Question 8

Evaluate $$100^2$$ \cdot \left(\dfrac{1}{4}\$$right)^2.$$

Accepted Answer

$$25^2$$

Question 9

Simplify $$\dfrac{x^2$ y^3$}{x^7$}.$$

Accepted Answer

$$\dfrac{y^3$}{x^5$}$$

Question 10

If there is a negative exponent in a fraction, what does it indicate?

Accepted Answer

The base is in the wrong part of the fraction and should be moved to the other side.

Question 11

Which of the following is the correct simplification of $$(a^b)^c$$?

Accepted Answer

$$a^{bc}$$

Question 12

What is the result of $$4^3$$ \cdot $$4^2$$?

Accepted Answer

$$4^5$$

Question 13

Which of the following is a correct application of the exponent rule for multiplying powers with the same base?

Accepted Answer

$$x^2$$ \cdot $$x^3$$ = $$x^5$$

Question 14

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

Accepted Answer

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

Question 15

If $$x^{-3}$$ $$y^2 is $$rewritten with only positive exponents, what is the result?

Accepted Answer

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

Exponents and Their Properties

Study Guide - Practice Questions