Question
Compute the following and simplify your answer. \[ \left(\frac{5}{x}\right)^{5} \] After simplifying, \( \left(\frac{5}{x}\right)^{5}=\square \). (Type exponential notation with positive exponents.)
Ask by Bird Little. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(\left(\frac{5}{x}\right)^{5} = \frac{3125}{x^{5}}\)
Solution
To simplify \(\left(\frac{5}{x}\right)^{5}\), follow these steps:
\[
\left(\frac{5}{x}\right)^{5} = \frac{5^{5}}{x^{5}} = \frac{3125}{x^{5}}
\]
After simplifying, \( \left(\frac{5}{x}\right)^{5} = \frac{3125}{x^{5}} \).
\(\boxed{\dfrac{3125}{x^{5}}}\)
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Simplify this solution Beyond the Answer
To simplify \( \left(\frac{5}{x}\right)^{5} \), we apply the power of a fraction rule that states \( \left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}} \). Thus, we have: \[ \left(\frac{5}{x}\right)^{5} = \frac{5^{5}}{x^{5}} \] Next, we compute \( 5^{5} \): \[ 5^{5} = 5 \times 5 \times 5 \times 5 \times 5 = 3125 \] Putting this all together, we get: \[ \left(\frac{5}{x}\right)^{5} = \frac{3125}{x^{5}} \] So the simplified answer is: \[ \left(\frac{5}{x}\right)^{5} = \frac{3125}{x^{5}} \]
