What is (x/(y^{1/2)}+(y^{1/2})/x)^5 ?

The solution to (x/(y^{1/2)}+(y^{1/2})/x)^5 is ((x^2+y)^5)/(x^5y^{5/2)}

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simplify (x/(y^{1/2)}+(y^{1/2})/x)^5

simplify

(\frac{x}{y ^{\frac{1}{2}}} + \frac{y ^{\frac{1}{2}}}{x})^{5}

\frac{( x ^{2} + y ) ^{5}}{x ^{5} y ^{\frac{5}{2}}}

Solution steps

(\frac{x}{y ^{\frac{1}{2}}} + \frac{y ^{\frac{1}{2}}}{x})^{5}

Join

\frac{x}{y ^{\frac{1}{2}}} + \frac{y ^{\frac{1}{2}}}{x} : \frac{x ^{2} + y}{x y ^{\frac{1}{2}}}

= (\frac{x ^{2} + y}{x y ^{\frac{1}{2}}})^{5}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( x ^{2} + y ) ^{5}}{( x y ^{\frac{1}{2}} ) ^{5}}

Simplify

(x y^{\frac{1}{2}})^{5} : x^{5} y^{\frac{5}{2}}

= \frac{( x ^{2} + y ) ^{5}}{x ^{5} y ^{\frac{5}{2}}}

\frac{x + 1}{3} + \frac{x + 2}{7} = 2

\frac{2}{3} \cdot 15

r^{2} + 12 r + 27 = 0

2 (x + 4) = 12

2 lo g_{5} (x) + lo g_{5} (3)

What is (x/(y^{1/2)}+(y^{1/2})/x)^5 ?
The solution to (x/(y^{1/2)}+(y^{1/2})/x)^5 is ((x^2+y)^5)/(x^5y^{5/2)}