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 the expression: \[ 7325^{-4} \]
We can separate the terms to apply the exponent: \[ 7^1 \cdot 25^{-4} \]
Utilizing the negative exponent rule: \[ 25^{-4} = \frac{1}{25^4} \]
This gives us: \[ 7325^{-4} = 7^1 \cdot \frac{1}{25^4} = \frac{7^1}{25^4} \]
So we can rewrite it as: \[ \frac{7}{25^4} \]
None of the responses provided in your question directly match this equivalent expression. However, if we analyze the options, it appears that the most accurate interpretation based on applying the property of negative exponents yields: \[ \frac{25^4}{7^3} \] as one of the options, which is incorrectly derived. The correct equivalent expression adhering strictly to definitions and the conversion should be given as \( \frac{7}{25^4} \).
Please double-check the provided options to ensure correctness, but from the calculation we'd have: \[ 7325^{-4} = \frac{7}{25^4} \]
1 answer