Question

Use the Product Rule of Exponents to simplify the expression 75⋅72
.)

Answer 1

To simplify the expression \( 7^5 \cdot 7^2 \) using the Product Rule of Exponents, we can apply the rule which states:

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

In this case, we have:

- \( a = 7 \)
- \( m = 5 \)
- \( n = 2 \)

Now, we can add the exponents:

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

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