Which of the following correctly use the product rule of exponents to simplify the expression 100 with a small eight on the top. 100 with a small seven on top. Would it be 100 with a small 15 on the top or 200 with a small 15 on top or 100 with a small 56 on top or 10,000 with a small 15 on top?

Answer 1

To simplify the expression \( 100^8 \cdot 100^7 \) using the product rule of exponents, you add the exponents.

According to the product rule:

\[ a^m \cdot a^n = a^{m+n} \]

In this case, \( a = 100 \), \( m = 8 \), and \( n = 7 \). Applying the product rule:

\[ 100^8 \cdot 100^7 = 100^{8+7} = 100^{15} \]

So, the correct simplification is \( 100 \) with a small \( 15 \) on top, which is \( 100^{15} \).

The answer is 100 with a small 15 on top.