To find an equivalent expression to \( 7325^{-4} \) with only positive exponents, we will apply the property of negative integer exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[ 7325^{-4} \]
We can rewrite this using the property mentioned:
\[ 7325^{-4} = \frac{1}{7325^4} \]
Next, we can break it down further:
\[ 7325^4 = (7^3 \cdot 25)^4 = 7^{3 \cdot 4} \cdot 25^4 = 7^{12} \cdot 25^4 \]
Thus, we have:
\[ 7325^{-4} = \frac{1}{7325^4} = \frac{1}{7^{12} \cdot 25^4} = 7^{-12} \cdot 25^{-4} \]
Now, we want an expression that only contains positive exponents. To express the terms with negative exponents in a positive form, we can write \( 7^{-12} \) as \( \frac{1}{7^{12}} \), and \( 25^{-4} \) as \( \frac{1}{25^4} \):
\[ = \frac{25^4}{7^{12}} \]
This is not in the same format as those provided in the options, but we can group them together into a single fraction:
\[ = \frac{25^4}{7^{12}} = 25^4 \cdot 7^{-12} \]
So, if we compare this with the responses, let's analyze each one manually:
- 25473 Start Fraction 25 superscript 4 baseline over 7 cubed end fraction - This is not correct as the exponent of 7 should be 12, not 3.
- 73⋅254 - This is not correct due to consistent calculations not matching the expression.
- 7 cubed times 25 superscript 4 baseline - Incorrect due to the exponent mismatch again.
- 2547−3 Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction - Again, incorrect due to exponent mismatch.
- 73254 - Incorrect as it doesn’t match our simplified positive expression.
Given that none of the responses match the equivalently simplified expression derived, the answer to the equivalent expression cannot be definitively chosen from the provided options. The best proper simplification remains \( \frac{25^4}{7^{12}} \) or similar forms that have positive exponents.
None match exactly what's derived from the initial expression using the property of negative exponents.
1 answer