What is ([(x-y)^{-3}]^n)/([(x+y)^n]^3) ?

The solution to ([(x-y)^{-3}]^n)/([(x+y)^n]^3) is 1/((x-y)^{3n)(x+y)^{3n}}

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simplify ([(x-y)^{-3}]^n)/([(x+y)^n]^3)

simplify

\frac{[ ( x - y ) ^{- 3} ] ^{n}}{[ ( x + y ) ^{n} ] ^{3}}

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

Solution steps

\frac{( ( x - y ) ^{- 3} ) ^{n}}{( ( x + y ) ^{n} ) ^{3}}

Simplify

((x - y)^{- 3})^{n} : \frac{1}{( x - y ) ^{3 n}}

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

Apply the fraction rule:

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

((x + y)^{n})^{3} = (x + y)^{n \cdot 3}

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

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

(a + b)^{- 3}

\frac{1}{5} - \frac{3}{5} \frac{x ^{5}}{2} + \frac{1}{4}

t - 3 t + 7 t

[x^{4} - 2 x^{2}]^{2} - 1

36 x^{2} - 4 x y + (\frac{y ^{2}}{9})

What is ([(x-y)^{-3}]^n)/([(x+y)^n]^3) ?
The solution to ([(x-y)^{-3}]^n)/([(x+y)^n]^3) is 1/((x-y)^{3n)(x+y)^{3n}}