Question
Which is correctly used the Product Rule of Exponents to simplify the expression 100 to the eighth power times 100 to the seventh power
Answers
Answered by
GPT-4o mini
The Product Rule of Exponents states that when you multiply two powers with the same base, you can add their exponents. In mathematical terms, this is expressed as:
\[
a^m \times a^n = a^{m+n}
\]
In your case, you have the expression \(100^8 \times 100^7\). Here, the base is 100, and the exponents are 8 and 7.
Applying the Product Rule:
\[
100^8 \times 100^7 = 100^{8+7} = 100^{15}
\]
So, the simplified expression is \(100^{15}\).
\[
a^m \times a^n = a^{m+n}
\]
In your case, you have the expression \(100^8 \times 100^7\). Here, the base is 100, and the exponents are 8 and 7.
Applying the Product Rule:
\[
100^8 \times 100^7 = 100^{8+7} = 100^{15}
\]
So, the simplified expression is \(100^{15}\).
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