Question

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

Answer 1

To simplify the expression \( 75 \cdot 72 \) using the Product Rule of Exponents, we start by recognizing that the bases are the same. The Product Rule states that when multiplying two powers with the same base, you can add their exponents:

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

In this case, the base is \( 7 \) and we have:

\[
75 \cdot 72 = 7^5 \cdot 7^2
\]

Applying the Product Rule, we add the exponents:

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

Thus, the simplified expression is:

\[
\boxed{7^7}
\]