Question
Simplify the expression completely: \( \left(\frac{x^{9}}{x^{5}}\right)^{4} \) Answer \( =\square \)
Ask by Moran Lynch. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{16} \)
Solution
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The Deep Dive
To simplify the expression \(\left(\frac{x^{9}}{x^{5}}\right)^{4}\), start by applying the quotient rule of exponents. This means you subtract the exponents in the fraction: \[ \frac{x^{9}}{x^{5}} = x^{9-5} = x^{4} \] Now raise this result to the power of 4: \[ \left(x^{4}\right)^{4} = x^{4 \cdot 4} = x^{16} \] So, the final simplified expression is: \[ \boxed{x^{16}} \]
