Use the Product Rule of Exponents to simplify 510⋅55

Question

(1 point)
Responses

550
5 superscript 50 baseline

2550
25 superscript 50 baseline

2515
25 superscript 15 baseline

515

Answer 1

To simplify \( 5^{10} \cdot 5^{5} \) using the Product Rule of Exponents, we can add the exponents since the bases are the same.

The Product Rule states that \( a^m \cdot a^n = a^{m+n} \).

Applying this to our expression:

\[ 5^{10} \cdot 5^{5} = 5^{10+5} = 5^{15} \]

Therefore, the correct answer is:

\[ 5^{15} \]

So the response would be \( 5^{15} \).