Negative Integer Exponents Quick Check

Question

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Question
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)
Responses

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

73⋅254
7 cubed times 25 superscript 4 baseline

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

25473

Answer 1

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

Starting with the expression:

\[ 7325^{-4} \]

we can rewrite this as:

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

Thus, the expression in terms of only positive exponents is:

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

From the options provided, this corresponds to:

\( \frac{7^3}{25^4} \)

So, the correct response is:

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