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?(1 point)

Question

Responses

7^3/25^4
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction

25^4/7^−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction

25^4/7^3
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction

7^3⋅25^4

Answer 1

To convert the expression \( \frac{7^3}{25^{-4}} \) into an equivalent expression with only positive exponents, we need to apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the original expression:

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

we can rewrite \( 25^{-4} \) as \( \frac{1}{25^4} \):

\[ \frac{7^3}{\frac{1}{25^4}} \]

When you divide by a fraction, it is equivalent to multiplying by its reciprocal:

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

Now, let's look at the options provided:

1. \( \frac{7^3}{25^4} \)
2. \( \frac{25^4}{7^{-3}} \)
3. \( \frac{25^4}{7^3} \)
4. \( 7^3 \cdot 25^4 \)

From our calculations, we found that the expression with only positive exponents is:

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

Thus, the correct response is:

\( 7^3 \cdot 25^4 \)