Which of the following is an equivalent expression to 7325−4

Question

with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses

73⋅254
7 cubed times 25 superscript 4 baseline

25473
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction

73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction

2547−3

Answer 1

To rewrite the expression \( 7325^{-4} \) with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the expression:

\[ 7325^{-4} = \frac{7325}{25^4} \]

To break it down further, we can express \( 7325 \) as \( 7^3 \times 25^4 \) based on the notation. Thus, the equivalent expression becomes:

\[ 7325^{-4} = \frac{7^3}{25^4} \]

This simplifies to:

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

Now, let's evaluate the responses:

1. \( 73 \cdot 254 \) - This is not the same form.
2. \( \frac{25^4}{7^3} \) - This is the inverse and has negative exponent.
3. \( \frac{7^3}{25^4} \) - This matches our equivalent form.
4. \( 25^4 \cdot 7^{-3} \) - This includes a negative exponent.

Thus, the correct response that is equivalent to \( 7325^{-4} \) with only positive exponents is:

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