What is (sqrt(x)-1/(3x^2))^{10} ?

The solution to (sqrt(x)-1/(3x^2))^{10} is ((3sqrt(x)x^2-1)^{10})/(59049x^{20)}

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simplify (sqrt(x)-1/(3x^2))^{10}

simplify

(x - \frac{1}{3 x ^{2}})^{10}

\frac{( 3 x x ^{2} - 1 ) ^{10}}{59049 x ^{20}}

Solution steps

(x - \frac{1}{3 x ^{2}})^{10}

Simplify

x - \frac{1}{3 x ^{2}} : \frac{3 x x ^{2} - 1}{3 x ^{2}}

= (\frac{3 x x ^{2} - 1}{3 x ^{2}})^{10}

Apply exponent rule:

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

= \frac{( 3 x x ^{2} - 1 ) ^{10}}{( 3 x ^{2} ) ^{10}}

Simplify

(3 x^{2})^{10} : 59049 x^{20}

= \frac{( 3 x x ^{2} - 1 ) ^{10}}{59049 x ^{20}}

\frac{18 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

(x - 3) (x - 3)

- sin (x + y) (1 + \frac{d y}{d x})

2 (ln (7 + 43) - 3)

What is (sqrt(x)-1/(3x^2))^{10} ?
The solution to (sqrt(x)-1/(3x^2))^{10} is ((3sqrt(x)x^2-1)^{10})/(59049x^{20)}