Which of the following is an equivalent expression to the numerator of 7 to the third power with a denominator of 25 to the negative fourth power with only positive exponents, generated by applying the Property of Negative Integer Exponents?

Answer 1

To write the expression for the numerator of \( 7^3 \) with a denominator of \( 25^{-4} \) using only positive exponents, we can apply the Property of Negative Integer Exponents.

The expression you gave can be represented as:

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

By the Property of Negative Exponents, \( a^{-n} = \frac{1}{a^n} \), we can rewrite \( 25^{-4} \) as:

\[ 25^{-4} = \frac{1}{25^4} \]

Therefore, the overall expression becomes:

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

Now, using only positive exponents, this simplifies to:

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

Thus, the equivalent expression with only positive exponents is:

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