Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem R.2.75

Chapter 1, Problem R.2.75

Evaluate each expression. See Example 4. (-3)⁵

Verified step by step guidance

Recognize that the expression \((-3)^5\) means raising the number \(-3\) to the power of 5, which involves multiplying \(-3\) by itself 5 times.

Write the expression as a product: \((-3)^5 = (-3) \times (-3) \times (-3) \times (-3) \times (-3)\).

Recall the rule for powers of negative numbers: if the exponent is odd, the result will be negative; if even, the result will be positive.

Calculate the absolute value by multiplying 3 by itself 5 times: \(3^5 = 3 \times 3 \times 3 \times 3 \times 3\).

Apply the sign determined in step 3 to the result from step 4 to get the final value of \((-3)^5\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exponentiation of Negative Numbers

Raising a negative number to a power involves multiplying the number by itself repeatedly. If the exponent is odd, the result remains negative; if even, the result is positive. For example, (-3)⁵ means multiplying -3 by itself five times.

Order of Operations and Parentheses

Parentheses indicate that the operation inside should be performed first. In (-3)⁵, the negative sign is part of the base, so the entire number -3 is raised to the fifth power, not just 3.

Evaluating Powers

To evaluate a power like (-3)⁵, multiply the base by itself as many times as the exponent indicates: (-3) × (-3) × (-3) × (-3) × (-3). This step-by-step multiplication helps find the exact value.

Recommended video:

03:41

Powers Of Complex Numbers In Polar Form (DeMoivre's Theorem)

Related Practice

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 6 • 12 + 6 • 15 = 6(12 + 15)

Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. -p² - 7q + r

views

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. (5x) • (1/5x) = 5 ( x • 1/x )

Textbook Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 2 (x - 3y + 2z)

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. (7.5 - y) + 0 = 7.5 - y

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. (t - 6) • ( 1/(t-6)) = 1, if t - 6 ≠ 0

views