Which expression is correctly developed to use the Product Rule of Exponents?(1 point) Responses (52)9 left parenthesis 5 squared right parenthesis superscript 9 baseline 62⋅73 6 squared times 7 cubed 108⋅108 10 superscript 8 baseline times 10 superscript 8 baseline 327

Answer 1

The Product Rule of Exponents states that when you multiply two expressions with the same base, you add the exponents. In other words, \( a^m \times a^n = a^{m+n} \).

Looking at your options, let’s identify the correct expression that uses the Product Rule of Exponents:

1. \( 9(5^2)^9 \) does not apply the Product Rule as it does not involve multiplying two terms with the same base.
2. \( 6^2 \cdot 7^3 \) does not involve the same base, so the Product Rule is not applicable here.
3. \( 10^8 \times 10^8 \) uses the Product Rule because both terms have the same base (10). According to the rule, it simplifies to \( 10^{8+8} = 10^{16} \).
4. \( 3^27 \) does not involve multiplication with another term, so the Product Rule does not apply here.

Thus, the correct expression that properly applies the Product Rule of Exponents is:

\( 10^8 \times 10^8 \).