Free preview

1.2 Exponents and Radicals

Focus on exponent rule and negative exponent.

Before you solve

Ideas in this lesson

Review the ideas below. Select one to see worked steps and five practice questions.

Lesson brief and rules

1.2 Exponents and Radicals

For the same nonzero base, add exponents when multiplying; $\sqrt{a^{2}}=|a|$ .

Worked example

1

01 / Simplify

x^{3}x^{5}x^{3}

as one power. Also identify the base and exponent in the first factor and write that factor as repeated multiplication.

02 / All factors have the same base

x

03 / Add the three exponents:

3+5+3=11

04 / The product is

x^{11}

05 / The base is the repeated factor

x

; the exponent

3

counts three copies of that factor.

Worked example 2 · Laws of exponents

Expand the power $(2x^{4}y^{2})^{3}$ .

The outer power applies to the coefficient and each variable factor.
Compute $2^{3}=8$ and $(x^{4})^{3}=x^{12}$ .
Also $(y^{2})^{3}=y^{6}$ , so the result is $8 x^{12} y^{6}$ .

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

Read this lesson preview

MathLab with Mr. Ahmed

1.2 Exponents and Radicals

Ideas in this lesson

1.2 Exponents and Radicals