Question

Simplify the following expression.

5^3 x 5^-5

A. 1/25
B. 25
C. 625
D. 1/5

Answer 1

can you double check

Answer 2

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**

Answer 3

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**