Question 1

Which of the following numbers is irrational?

Accepted Answer

$$\sqrt{7}$$

Question 2

Simplify the expression $$6 \div 3 \cdot 2$$ using the correct order of operations.

Accepted Answer

$$2$$

Question 3

Which property is illustrated by the equation $$a + (b + c) = (a + b) + c$$?

Accepted Answer

Associative Property

Question 4

Rewrite $$x^{\frac{5}$${3}}$$ in radical form.

Accepted Answer

$$\sqrt[3]{x^5$}$$

Question 5

What is the simplified form of $$\dfrac{a^7$}{a^3$}$$?

Accepted Answer

$$a^4$$

Question 6

If $$a^0 is $$evaluated, what is the result (assuming $$a 
eq 0$$)?

Accepted Answer

$$1$$

Question 7

Which of the following is the correct application of the power of a product property for $$(ab)^n$$?

Accepted Answer

$$a^n b^n$$

Question 8

Simplify the expression $$\left(\dfrac{x^2$ y^3$}{z^4$}\$$right)^5$$.

Accepted Answer

$$\dfrac{x$$^{10}$$ y$$^{15}$$}{z$$^{20}$$}$$

Question 9

Which of the following is a real number but NOT a rational number?

Accepted Answer

$$\pi$$

Question 10

Evaluate $$7[12 - 5 	imes 6]$$ using the correct order of operations.

Accepted Answer

$$-1176$$

Question 11

Express $$\sqrt[4]{n^7$} in $$exponential form.

Accepted Answer

$$n^{7/4}$$

Question 12

Simplify $$\dfrac{27x^7$ y$$^{11}$$}{8x^5$}.$$

Accepted Answer

$$\dfrac{27y$$^{11}$$}{8x$$^{2}$$}$$

Question 13

Which property is illustrated by $$a \cdot 1 = a$$?

Accepted Answer

Identity Property

Question 14

Simplify $$\$$left(a^{4}$$b^{5}$$\$$right)^{2}$.

Accepted Answer

$$a^{8}b$$^{10}$

Question 15

Which of the following is the correct definition of a rational number?

Accepted Answer

A number that can be written as $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q 
eq 0$$

Question 16

Simplify $$\dfrac{4x^7$}{2x^5$}.$$

Accepted Answer

$$2x^{2}$$

Question 17

What is the result of $$\$$left(b^{4}$$\$$right)^{\frac{1}$${2}}$$?

Accepted Answer

$$b^{2}$$

Question 18

Which property allows you to write $$a(b + c) = ab + ac$$?

Accepted Answer

Distributive Property

Question 19

Simplify $$\left(\dfrac{2x^3$}{y^2$}\$$right)^{-4}$$ and write with positive exponents.

Accepted Answer

$$\dfrac{y$$^{8}$$}{16x$$^{12}$$}$$

Question 20

Which of the following is the correct exponential form of $$\sqrt{5y}$$?

Accepted Answer

$$(5y)^{1/2}$$

Real Numbers, Properties, and Exponents: Foundations for Statistics

Study Guide - Practice Questions