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

options:

32^7

(5^2)^9

10^8 ⋅ 10^8

6^2 ⋅ 7^3

1 answer

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.