Question

Find the numerical equivalent of 5^10 ⋅ 5^−6 The answer should not contain any exponent expression or decimals. Show your work.

Answer 1

To simplify the expression \( 5^{10} \cdot 5^{-6} \), we can apply the property of exponents that states:

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

In this case, we have:

\[
5^{10} \cdot 5^{-6} = 5^{10 + (-6)} = 5^{10 - 6} = 5^4
\]

Now, we need to find the numerical value of \( 5^4 \).

Calculating \( 5^4 \):

\[
5^4 = 5 \times 5 \times 5 \times 5
\]

Calculating step by step:

1. \( 5 \times 5 = 25 \)
2. \( 25 \times 5 = 125 \)
3. \( 125 \times 5 = 625 \)

Thus, \( 5^4 = 625 \).

So, the numerical equivalent of \( 5^{10} \cdot 5^{-6} \) is

\[
\boxed{625}
\]