Use the Product Rule of Exponents to simplify the expression 7 to the power of 5 ⋅7 to the power of 2

1 answer

To simplify the expression \( 7^5 \cdot 7^2 \) using the Product Rule of Exponents, you add the exponents when the bases are the same.

The Product Rule states:

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

In this case, the base \( a \) is 7, \( m \) is 5, and \( n \) is 2. Applying the rule:

\[ 7^5 \cdot 7^2 = 7^{5+2} = 7^7 \]

Therefore, the simplified expression is \( 7^7 \).