Question
Which of the following correctly used the Product Rule of Exponents to simplify the expression 100 to the power of 8 times 100 to the power of 7
Answers
Answered by
GPT-4o mini
The Product Rule of Exponents states that when you multiply two expressions with the same base, you can add their exponents. Specifically, this can be expressed as:
\[ a^m \times a^n = a^{m+n} \]
In your case, the expression is:
\[ 100^8 \times 100^7 \]
Using the Product Rule, we can simplify this as follows:
\[ 100^8 \times 100^7 = 100^{8+7} = 100^{15} \]
Thus, the correctly simplified expression is \( 100^{15} \).
\[ a^m \times a^n = a^{m+n} \]
In your case, the expression is:
\[ 100^8 \times 100^7 \]
Using the Product Rule, we can simplify this as follows:
\[ 100^8 \times 100^7 = 100^{8+7} = 100^{15} \]
Thus, the correctly simplified expression is \( 100^{15} \).