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