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. $\text{Missing superscript or subscript argument}$ - 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:

$$\boxed{{\displaystyle 7^3\cdot {25}^4}}$$