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?

Question

7^3 x 25^4
25^4/7^-3
25^4/7^3
7^3/25^4

Answer 1

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

Starting with \( \frac{7^3}{25^{-4}} \):

1. Rewrite \( 25^{-4} \) as \( \frac{1}{25^4} \): \[ \frac{7^3}{25^{-4}} = 7^3 \cdot 25^4 \]

Now, we have expressed the original expression using only positive exponents:

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

Thus, the equivalent expression to \( \frac{7^3}{25^{-4}} \) with only positive exponents is:

7^3 x 25^4