Which of the following is an equivalent expression to 7^3 over 25^−4

Question

with only positive exponents, generated by applying the Property of Negative Integer Exponents?

options:

25^4 over 73^

7^3 over 25^4

25^4 over 7^−3

7^3 ⋅ 25^4

Answer 1

To simplify the expression \( \frac{7^3}{25^{-4}} \) using the property of negative integer exponents, we apply the rule that states \( a^{-n} = \frac{1}{a^n} \).

This means that \( 25^{-4} \) can be rewritten as \( \frac{1}{25^4} \). Thus, the expression becomes:

\[ \frac{7^3}{25^{-4}} = 7^3 \cdot 25^{4} \]

Now, let's evaluate the options provided:

1. \( \frac{25^4}{73^} \) - This option contains an error in notation (73^).
2. \( \frac{7^3}{25^4} \) - This is not equivalent, as we need to deal with the negative exponent.
3. \( \frac{25^4}{7^{-3}} \) - This is not equivalent, as we also have the negative exponent issue.
4. \( 7^3 \cdot 25^4 \) - This is the correct expression we derived.

Thus, the equivalent expression with only positive exponents is:

\[ \boxed{7^3 \cdot 25^4} \]