Which expression is correctly developed to use the Product Rule of Exponents?

Question

options:

32^7

(5^2)^9

10^8 ⋅ 10^8

6^2 ⋅ 7^3

Answer 1

The Product Rule of Exponents states that when you multiply two expressions that have the same base, you can add their exponents. The standard form of the Product Rule is:

\[ a^m \cdot a^n = a^{m+n} \]

From the provided options, the expression that can be correctly developed using the Product Rule of Exponents is:

10^8 ⋅ 10^8

Using the Product Rule, this would be simplified as follows:

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

The other options do not represent expressions that involve the multiplication of the same base.