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)

Question

7^3/25^4

7^3⋅25^4

25^4/7^3

25^4/7−3

Answer 1

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