Question

Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses

327
32 superscript 7 baseline

(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline

108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline

62⋅73

Answer 1

The Product Rule of Exponents states that when you multiply two expressions with the same base, you can add their exponents. That is, \( a^m \cdot a^n = a^{m+n} \).

Let's evaluate each response:

1. **\( 327 \)**: This is just a number and does not involve exponents.
2. **\( 32^7 \)**: This expression does not involve the multiplication of two bases with exponents, so it does not apply the Product Rule.
3. **\( (5^2)^9 \)**: This uses the Power of a Power Rule \( (a^m)^n = a^{mn} \), not the Product Rule.
4. **\( 10^8 \cdot 10^8 \)**: This expression applies the Product Rule because it involves multiplying two identical bases: \( 10^8 \cdot 10^8 = 10^{8+8} = 10^{16} \).
5. **\( 6^2 \cdot 7^3 \)**: This does not apply the Product Rule since the bases are different (6 and 7).

The correct expression that uses the Product Rule of Exponents is:

**\( 10^8 \cdot 10^8 \)**.