Which expression is correctly developed to use the Product Rule of Exponents?(1 point)

Question

Responses

32^7
32 superscript 7 baseline

10^8⋅10^8
10 superscript 8 baseline times 10 superscript 8 baseline

(5^2)^9
left parenthesis 5 squared right parenthesis superscript 9 baseline

6^2⋅7^3

Answer 1

The Product Rule of Exponents states that when multiplying two expressions with the same base, you can add the exponents. Therefore, to correctly apply the Product Rule, we need to identify an expression of the form \(a^m \cdot a^n\).

Among the given expressions, the one that can be directly developed using the Product Rule is:

10^8⋅10^8 (10 superscript 8 baseline times 10 superscript 8 baseline)

This expression uses the same base (10), and you can apply the Product Rule of Exponents by adding the exponents:

\[ 10^8 \cdot 10^8 = 10^{8 + 8} = 10^{16}. \]

The other options do not have a scenario that utilizes the Product Rule directly.