Which of the following is an equivalent expression to 7325−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)

7^3/25^4

7^3⋅25^4

25^4/7^3

25^4/7−3

1 answer

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

Starting with \( 7325^{-4} \):

  1. We can express this as: \[ 7325^{-4} = \frac{1}{7325^4} \]

  2. Recognizing that \( 7325 = 7^3 \cdot 25^4 \) allows us to rewrite it: \[ 7325^4 = (7^3 \cdot 25^4)^4 = (7^3)^4 \cdot (25^4)^4 = 7^{12} \cdot 25^{16} \]

  3. However, a more straightforward way to present this in terms of the options provided is simply using the property of the negative exponent without expanding explicitly: \[ 7325^{-4} = \frac{1}{7^3 \cdot 25^4} \]

Thus, using the property directly with the original expression, we see that:

\[ 7325^{-4} = \frac{1}{7^3 \cdot 25^4} = \frac{25^4}{7^3} \]

Among the options provided, the equivalent expression using only positive exponents is:

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

Thus, the correct answer is:

25^4/7^3