What is (x^{-3}+y^3)^{-7} ?

The solution to (x^{-3}+y^3)^{-7} is (x^{21})/((x^3y^3+1)^7)

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simplify (x^{-3}+y^3)^{-7}

simplify

(x^{- 3} + y^{3})^{- 7}

\frac{x ^{21}}{( x ^{3} y ^{3} + 1 ) ^{7}}

Solution steps

(x^{- 3} + y^{3})^{- 7}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(x^{- 3} + y^{3})^{- 7} = \frac{1}{( x ^{- 3} + y ^{3} ) ^{7}}

= \frac{1}{( x ^{- 3} + y ^{3} ) ^{7}}

Simplify

(x^{- 3} + y^{3})^{7} : \frac{( y ^{3} x ^{3} + 1 ) ^{7}}{x ^{21}}

= \frac{1}{\frac{( y ^{3} x ^{3} + 1 ) ^{7}}{x ^{21}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x ^{21}}{( x ^{3} y ^{3} + 1 ) ^{7}}

4 \times 24

20 + 35 - 2500

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(3 x + 4) (2 x + 10)

6 x - 2 x^{2}

What is (x^{-3}+y^3)^{-7} ?
The solution to (x^{-3}+y^3)^{-7} is (x^{21})/((x^3y^3+1)^7)