Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8 ⋅ 100^7?

Question

10,000^15

100^15

200^15

100^56

Answer 1

To simplify the expression \( 100^8 \cdot 100^7 \) using the Product Rule of Exponents, we use the property that states \( a^m \cdot a^n = a^{m+n} \).

So, we have: \[ 100^8 \cdot 100^7 = 100^{8+7} = 100^{15}. \]

Now, let's look at the options given:

1. \( 10,000^{15} \) - This is not correct.
2. \( 100^{15} \) - This is the correct simplification.
3. \( 200^{15} \) - This is not correct.
4. \( 100^{56} \) - This is not correct.

Thus, the correct answer is \( \boxed{100^{15}} \).