What is (sqrt(x^{-3)})^5 ?

The solution to (sqrt(x^{-3)})^5 is 1/(x^7sqrt(x))

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simplify (sqrt(x^{-3)})^5

simplify

(x^{- 3})^{5}

\frac{1}{x ^{7} x}

Solution steps

(x^{- 3})^{5}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x^{- 3})^{4 + 1} = (x^{- 3})^{4} x^{- 3}

= (x^{- 3})^{4} x^{- 3}

Simplify

(x^{- 3})^{4} : ((x^{- 3})^{2})^{2}

= ((x^{- 3})^{2})^{2} x^{- 3}

Apply exponent rule:

assuming

n i s o dd or a \geq 0

(x^{- 3})^{2} = x^{- 3}

= (x^{- 3})^{2} x^{- 3}

Simplify

(x^{- 3})^{2} : \frac{1}{x ^{6}}

= \frac{1}{x ^{6}} x^{- 3}

Simplify

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

= \frac{1}{x ^{6}} \cdot \frac{1}{x x}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{x ^{6} x x}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{x ^{6} x x}

Simplify

x^{6} x : x^{7}

= \frac{1}{x ^{7} x}

arctan (\frac{( 1 + x ^{2} + 1 )}{x})

(3 x^{2} + x)^{3}

(\frac{4 a}{5 - 2})^{3}

x^{2} + 2 x + x + 2

22 \cdot x^{3} + 33 \cdot y^{3}