Use the Product Rule of Exponents to simplify the expression 7^5 . 7^2

1 answer

To simplify the expression \( 7^5 \cdot 7^2 \) using the Product Rule of Exponents, we apply the rule which states that when multiplying two exponents with the same base, you add the exponents:

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

In this case, \( a = 7 \), \( m = 5 \), and \( n = 2 \). Therefore, we have:

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

So, the simplified expression is:

\[ 7^7 \]