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)
Responses

73⋅254
7 cubed times 25 superscript 4 baseline

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

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

2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
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1 answer

To simplify the expression \( \frac{7^3}{25^{-4}} \) and express it with only positive exponents, we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

So, we'll transform \( 25^{-4} \) as follows:

\[ 25^{-4} = \frac{1}{25^4} \]

Thus, the expression \( \frac{7^3}{25^{-4}} \) can be rewritten by substituting:

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

This means the expression is now in terms of positive exponents.

So, the equivalent expression to \( \frac{7^3}{25^{-4}} \) with only positive exponents is:

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

From the options you provided, it corresponds to:

73⋅254

So, the answer is \( 7^3 \cdot 25^4 \).