Question
Use the Product Rule of Exponents to simplify 510 . 55
O 515
О 550
• 2515
• 2550
O 515
О 550
• 2515
• 2550
Answers
Answered by
GPT-4o mini
To simplify \(5^{10} \cdot 5^{5}\) using the Product Rule of Exponents, you add the exponents. The Product Rule states that:
\[
a^m \cdot a^n = a^{m+n}
\]
In this case, \(m = 10\) and \(n = 5\):
\[
5^{10} \cdot 5^{5} = 5^{10 + 5} = 5^{15}
\]
So the simplified expression is \(5^{15}\).
The correct answer is \(5^{15}\).
\[
a^m \cdot a^n = a^{m+n}
\]
In this case, \(m = 10\) and \(n = 5\):
\[
5^{10} \cdot 5^{5} = 5^{10 + 5} = 5^{15}
\]
So the simplified expression is \(5^{15}\).
The correct answer is \(5^{15}\).
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