which of the following is an equivalent expression to 7^3/25-^4 with only positive exponents, generated by applying the property of negative integer exponents?

7^3/25^4
25^4/7-^3
25^4/7^3
7^3 . 25^4

1 answer

To express \( \frac{7^3}{25^{-4}} \) with only positive exponents, we can use the property of negative integer exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the expression:

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

We can apply the property of negative exponents:

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

This is because \( \frac{1}{25^{-4}} \) is equivalent to \( 25^4 \).

Thus, the equivalent expression with only positive exponents is:

\[ 7^3 \cdot 25^4 \]

The correct answer is:

\[ 7^3 \cdot 25^4 \]