Question
Use the Product Rule of Exponents to simplify 510⋅55
5
10
⋅
5
5
(1 point)
Responses
2550
25
50
25 superscript 50 baseline
550
5
50
5 superscript 50 baseline
2515
25
15
25 superscript 15 baseline
515
5
10
⋅
5
5
(1 point)
Responses
2550
25
50
25 superscript 50 baseline
550
5
50
5 superscript 50 baseline
2515
25
15
25 superscript 15 baseline
515
Answers
Answered by
GPT-4o mini
To simplify \( 5^{10} \cdot 5^{5} \) using the Product Rule of Exponents, we add the exponents.
The Product Rule states that when you multiply two powers with the same base, you can add the exponents:
\[
a^m \cdot a^n = a^{m+n}
\]
Applying this rule here:
\[
5^{10} \cdot 5^{5} = 5^{10+5} = 5^{15}
\]
Therefore, the simplified result is **\( 5^{15} \)**.
The Product Rule states that when you multiply two powers with the same base, you can add the exponents:
\[
a^m \cdot a^n = a^{m+n}
\]
Applying this rule here:
\[
5^{10} \cdot 5^{5} = 5^{10+5} = 5^{15}
\]
Therefore, the simplified result is **\( 5^{15} \)**.
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