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Exercises Polynomials and factoring

Example 10.13 from Prealgebra, 10.2 Use Multiplication Properties of Exponents

Use Multiplication Properties of Exponents: example 10.13

Simplify:

ⓐ ${(−3)}^{4}$
ⓑ ${−3}^{4}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

ⓐ

${(−3)}^{4}$

Multiply four factors of −3. $(−3) (−3) (−3) (−3)$

Simplify. $81$

ⓑ

${−3}^{4}$

Multiply two factors. $- (3 \cdot 3 \cdot 3 \cdot 3)$

Simplify. $−81$

Notice the similarities and differences in parts ⓐ and ⓑ. Why are the answers different? In part ⓐ the parentheses tell us to raise the (−3) to the 4^th power. In part ⓑ we raise only the 3 to the 4^th power and then find the opposite.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify:

ⓐ ${(−2)}^{4}$
ⓑ ${−2}^{4}$

How did it go?

PreviousUse Multiplication Properties of Exponents: example 10.12 Next Use Multiplication Properties of Exponents: example 10.14

From Prealgebra (1st edition) by OpenStax (Rice University), section 10.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.