Question
The simplified form of the expression \( \sqrt[3]{\frac{8}{x^{9}}} \) is
Ask by Marsh Ray. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{2}{x^{3}} \)
Solution
Calculate or simplify the expression \( (8/x^9)^(1/3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\frac{8}{x^{9}}\right)^{\frac{1}{3}}\)
- step1: Rewrite the expression:
\(\frac{8^{\frac{1}{3}}}{\left(x^{9}\right)^{\frac{1}{3}}}\)
- step2: Evaluate the power:
\(\frac{2}{x^{3}}\)
The simplified form of the expression \( \sqrt[3]{\frac{8}{x^{9}}} \) is \( \frac{2}{x^{3}} \).
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Simplify this solution Mind Expander
To simplify the expression \( \sqrt[3]{\frac{8}{x^{9}}} \), we can rewrite it as \( \frac{\sqrt[3]{8}}{\sqrt[3]{x^{9}}} \). The cube root of 8 is 2, since \( 2^3 = 8 \). For the term \( \sqrt[3]{x^{9}} \), we can use the property of exponents to find that \( \sqrt[3]{x^{9}} = x^{9/3} = x^{3} \). So, the expression simplifies to \( \frac{2}{x^{3}} \). Thus, the final simplified form is: \[ \frac{2}{x^{3}} \]
