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

Question

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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 \( 7^7 \).