# We need to calculate: The simplified form of sqrt[5]{x^{2}y^{2}} cdot sqrt[4]{x}

necessaryh 2021-01-02 Answered
We need to calculate: The simplified form of
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## Expert Answer

rogreenhoxa8
Answered 2021-01-03 Author has 109 answers
Given:
The expression is
Formula used:
For a real number a when m is even,
$\sqrt[n]{{a}^{n}}=|{a}^{\frac{n}{m}}|$
Calculation:
Consider the provided expression:

Since, the radicals have different indices, the product property of radicals cannot be applied directly.
So, rewrite the expression with rational exponents:

Apply the power rule of exponents:

Add exponents of like bases:

$={x}^{\frac{17}{20}}{y}^{\frac{2}{5}}$
Writing each exponent with the same denominator, so that in radical notation, the factors will have the same index.
${x}^{\frac{17}{20}}{y}^{\frac{2}{5}}={x}^{\frac{17}{20}}{y}^{\frac{8}{20}}$

Convert to radical notation:
$\frac{\left({x}^{17}{y}^{8}{\right)}^{1}}{20}=\sqrt[20]{{x}^{17}{y}^{8}}$
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