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

\[ \boxed{625} \]