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

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

73⋅254
7 cubed times 25 superscript 4 baseline

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

2547−3

Answer 1

To rewrite the expression \( \frac{7^3}{25^{-4}} \) with only positive exponents, we'll use the property of negative exponents, which states that \( a^{-b} = \frac{1}{a^b} \).

1. Rewrite \( 25^{-4} \): \[ 25^{-4} = \frac{1}{25^4} \]

2. Substitute it back into the original expression: \[ \frac{7^3}{25^{-4}} = 7^3 \cdot 25^4 \]

Now, we can see that this expression \( 7^3 \cdot 25^4 \) is equivalent to the option:

73⋅254

So, the correct answer is: 7 cubed times 25 superscript 4 baseline.