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 x2y25  x4
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Expert Answer

rogreenhoxa8
Answered 2021-01-03 Author has 109 answers
Given:
The expression is x2y25  x4
Formula used:
For a real number a when m is even,
ann=|anm|
Calculation:
Consider the provided expression:
x2y25  x4
Since, the radicals have different indices, the product property of radicals cannot be applied directly.
So, rewrite the expression with rational exponents:
x2y25  x4=(x3y2)15  x14
Apply the power rule of exponents:
(x3y2)15  x(14)=x35 y25 x14
Add exponents of like bases:
x35 y25 x14=x(35 + 14)y25
=x(1220 + 520)y25
=x1720y25
Writing each exponent with the same denominator, so that in radical notation, the factors will have the same index.
x1720y25=x1720y820
= (x17y8)120
Convert to radical notation:
(x17y8)120=x17y820
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