Question

Writing  Use a property of exponents to write left parenthesis 2 a right parenthesis Superscript 5 as a product of powers. Use pencil and paper. Describe the property of exponents that you used. In​ words, what does the power of a product​ equal?
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Part 1
Choose the correct answer below.
A.left parenthesis 2 a right parenthesis Superscript 5 equals 2 a Superscript 5
left parenthesis 2 a right parenthesis Superscript 5equals2 a Superscript 5
B.left parenthesis 2 a right parenthesis Superscript 5 equals 2 Superscript 5 Baseline a Superscript 5
left parenthesis 2 a right parenthesis Superscript 5equals2 Superscript 5 Baseline a Superscript 5
C.left parenthesis 2 a right parenthesis Superscript 5 equals 2 Superscript 6 Baseline a Superscript 6
left parenthesis 2 a right parenthesis Superscript 5equals2 Superscript 6 Baseline a Superscript 6
D.left parenthesis 2 a right parenthesis Superscript 5 equals 2 Superscript 5 Baseline a
left parenthesis 2 a right parenthesis Superscript 5equals2 Superscript 5 Baseline a

Answer 1

Correct choice: B.

Reason: (2a)^5 = (2a)(2a)(2a)(2a)(2a) = (2·2·2·2·2)(a·a·a·a·a) = 2^5 a^5.

Property used: The power of a product equals the product of the powers; in symbols, (xy)^n = x^n y^n.