Question
Simplify. \( \left(\sqrt{2 x^{5}}\right)^{10} \) \( [?] x \)
Ask by Campbell Higgins. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( 32x^{25} \).
Solution
Calculate or simplify the expression \( (\sqrt{2x^5})^{10} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\sqrt{2x^{5}}\right)^{10}\)
- step1: Simplify the root:
\(\left(x^{2}\sqrt{2x}\right)^{10}\)
- step2: Evaluate the power:
\(\left(x^{2}\right)^{10}\left(\sqrt{2x}\right)^{10}\)
- step3: Evaluate the power:
\(x^{20}\left(\sqrt{2x}\right)^{10}\)
- step4: Evaluate the power:
\(x^{20}\times 32x^{5}\)
- step5: Calculate:
\(32x^{20}\times x^{5}\)
- step6: Multiply the terms:
\(32x^{25}\)
The simplified form of \( \left(\sqrt{2 x^{5}}\right)^{10} \) is \( 32x^{25} \).
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Simplify this solution Mind Expander
To simplify \( \left(\sqrt{2 x^{5}}\right)^{10} \), we can start by rewriting the square root as an exponent: \[ \sqrt{2 x^{5}} = (2 x^{5})^{1/2} \] Now, applying the exponent, we get: \[ \left( (2 x^{5})^{1/2} \right)^{10} = (2 x^{5})^{10/2} = (2 x^{5})^{5} \] Now we distribute the exponent: \[ (2)^{5} (x^{5})^{5} = 32 x^{25} \] So, the simplified expression is: \[ 32 x^{25} \]
