What is [((x^2)/2)-(2/x)]^4 ?

The solution to [((x^2)/2)-(2/x)]^4 is ((x^3-4)^4)/(16x^4)

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simplify [((x^2)/2)-(2/x)]^4

simplify

[(\frac{x ^{2}}{2}) - (\frac{2}{x})]^{4}

\frac{( x ^{3} - 4 ) ^{4}}{16 x ^{4}}

Solution steps

((\frac{x ^{2}}{2}) - (\frac{2}{x}))^{4}

Simplify

(\frac{x ^{2}}{2}) - (\frac{2}{x}) : \frac{x ^{2}}{2} - \frac{2}{x}

= (\frac{x ^{2}}{2} - \frac{2}{x})^{4}

Join

\frac{x ^{2}}{2} - \frac{2}{x} : \frac{x ^{3} - 4}{2 x}

= (\frac{x ^{3} - 4}{2 x})^{4}

Apply exponent rule:

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

= \frac{( x ^{3} - 4 ) ^{4}}{( 2 x ) ^{4}}

Simplify

(2 x)^{4} : 16 x^{4}

= \frac{( x ^{3} - 4 ) ^{4}}{16 x ^{4}}

(\frac{x + 1}{4})^{3}

(x - 4)^{8} \cdot (x - 4)^{2}

\frac{( 9 k ^{2} - 33 k + 10 )}{( 18 k ^{3} - 200 k )}

\frac{( x ^{3} - 4 x ^{2} + x + 6 )}{( x ^{2} - 2 x - 3 )}

(x + 2 y) (x + 2 y + 4) - 12

What is [((x^2)/2)-(2/x)]^4 ?
The solution to [((x^2)/2)-(2/x)]^4 is ((x^3-4)^4)/(16x^4)