Question
Simplify the following expression.
5^3 x 5^-5
A. 1/25
B. 25
C. 625
D. 1/5
5^3 x 5^-5
A. 1/25
B. 25
C. 625
D. 1/5
Answers
GPT-4o mini
To simplify the expression \( 5^3 \times 5^{-5} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
Applying this property:
\[
5^3 \times 5^{-5} = 5^{3 + (-5)} = 5^{3 - 5} = 5^{-2}
\]
Now, to express \( 5^{-2} \) in a more simplified form, we can rewrite it as:
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
Thus, the simplified expression is \( \frac{1}{25} \).
The correct answer is:
**A. 1/25**
Applying this property:
\[
5^3 \times 5^{-5} = 5^{3 + (-5)} = 5^{3 - 5} = 5^{-2}
\]
Now, to express \( 5^{-2} \) in a more simplified form, we can rewrite it as:
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
Thus, the simplified expression is \( \frac{1}{25} \).
The correct answer is:
**A. 1/25**
can you double check
GPT-4o mini
Certainly! Let's go through the steps again to double check the simplification of the expression \( 5^3 \times 5^{-5} \).
1. Use the property of exponents: \( a^m \times a^n = a^{m+n} \).
Here, we have:
\[
5^3 \times 5^{-5} = 5^{3 + (-5)} = 5^{3 - 5} = 5^{-2}
\]
2. Now, simplify \( 5^{-2} \):
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
So, upon re-evaluation, the simplification remains consistent. The final answer is indeed:
**A. 1/25**
1. Use the property of exponents: \( a^m \times a^n = a^{m+n} \).
Here, we have:
\[
5^3 \times 5^{-5} = 5^{3 + (-5)} = 5^{3 - 5} = 5^{-2}
\]
2. Now, simplify \( 5^{-2} \):
\[
5^{-2} = \frac{1}{5^2} = \frac{1}{25}
\]
So, upon re-evaluation, the simplification remains consistent. The final answer is indeed:
**A. 1/25**