Q: Which of the following is the correct application of the zero exponent rule?

$$a^0 = 1$ \text{ for } a \neq 0$

Question 1

Which of the following correctly expresses the meaning of the exponential expression $$x^n$$?

Accepted Answer

$$x^n$$ means $$x is $$multiplied by itself $$n$$ times: $$x \cdot x \cdot x \cdot \ldots \cdot x$$ ($$n$$ factors of $$x).$$

Question 2

Which of the following is an example of a linear equation in one variable?

Accepted Answer

$$2x + 5 = 7$$

Question 3

Which property of exponents is illustrated by the equation $$a^m \cdot a^n = a$$^{m+n}$$?

Accepted Answer

Product Rule for Exponents

Question 4

Simplify the expression $$(2x^3)^4$ using the power rule for exponents.

Accepted Answer

$$16x^{12}$$

Question 5

Which equation is NOT linear?

Accepted Answer

$$x^2 + 2x = 5$

Question 6

What is the least common denominator (LCD) of the fractions $$\frac{1}{4}$$ and $$\frac{1}{6}$$?

Accepted Answer

$$12$$

Question 7

Solve for $$x$$: $$\frac{2}{3}x - \frac{1}{6} = \frac{1}{2}.$$

Accepted Answer

$$x = 1.25$$

Question 8

Which property of equality justifies the step from $$x + 5 = 12 to$$ $$x = 7$$?

Accepted Answer

Addition Property of Equality

Question 9

Simplify the expression $$3x + 2x - 4.$$

Accepted Answer

$$5x - 4$$

Question 10

Which of the following is the correct application of the power of a quotient rule: $$\left(\frac{a}{b}\right)^n$$?

Accepted Answer

$$\frac{a^n}{b^n}$$

Question 11

Solve for $$x$$: $$0.2x + 0.5 = 1.1.$$

Accepted Answer

$$x = 3$$

Question 12

Which of the following is the correct application of the zero exponent rule?

Accepted Answer

$$a^0 = 1$ 	ext{ for } a 
eq 0$

Question 13

Which of the following is the correct simplification of $$\frac{a^5$}{a^2$}$$?

Accepted Answer

$$a^{3}$$

Question 14

A chemist needs to prepare a solution by mixing two chemicals. The equation $$0.3x + 0.7 = 2.2$$ models the amount of chemical $$x$$ needed. What is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 15

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

Accepted Answer

$$a^n b^n$$

Question 16

Which of the following equations is equivalent to $$\frac{1}{2}x + \frac{1}{3} = 1$$ after clearing fractions using the LCD?

Accepted Answer

$$3x + 2 = 6$$

Question 17

A patient is prescribed a medication where the dosage is modeled by the equation $$0.05x + 0.2 = 1.2. $$What is the correct value of $$x$$?

Accepted Answer

$$x = 20$$

Question 18

Which of the following is NOT a property of equality?

Accepted Answer

Zero Exponent Rule

Question 19

If $$x = 4 is a $$solution to the equation $$2x - 3 = 5$$, which property of equality was used to isolate $$x$$?

Accepted Answer

Multiplication Property of Equality

Question 20

Which of the following is the correct simplification of $$2(x + 3) - 4x$$?

Accepted Answer

$$-2x + 6$$

Linear Equations and Properties of Exponents: Foundations for College Algebra

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