Use the Product Rule of Exponents to simplify 510⋅55

Question

(1 point)
Responses

2550
25 superscript 50 baseline

2515
25 superscript 15 baseline

550
5 superscript 50 baseline

515

Answer 1

To simplify \( 5^{10} \cdot 5^5 \), we can use the Product Rule of Exponents, which states that when you multiply two powers with the same base, you add their exponents:

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

In this case:

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

So the simplified expression is:

\[ 5^{15} \]

Thus, the correct response is:

\( 5^{15} \)