What is (x/y)^{-2}*(x/y)^{-3}*(x/y) ?

The solution to (x/y)^{-2}*(x/y)^{-3}*(x/y) is (y^4)/(x^4)

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simplify (x/y)^{-2}(x/y)^{-3}(x/y)

simplify

(\frac{x}{y})^{- 2} \cdot (\frac{x}{y})^{- 3} \cdot (\frac{x}{y})

\frac{y ^{4}}{x ^{4}}

Solution steps

(\frac{x}{y})^{- 2} (\frac{x}{y})^{- 3} (\frac{x}{y})

Apply rule:

(a) = a

(\frac{x}{y}) = \frac{x}{y}

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

Apply exponent rule:

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

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

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

Add/Subtract the numbers:

- 2 - 3 + 1 = - 4

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

Apply exponent rule:

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

(\frac{x}{y})^{- 4} = \frac{1}{( \frac{x}{y} ) ^{4}}

= \frac{1}{( \frac{x}{y} ) ^{4}}

Apply exponent rule:

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

(\frac{x}{y})^{4} = \frac{x ^{4}}{y ^{4}}

= \frac{1}{\frac{x ^{4}}{y ^{4}}}

Apply the fraction rule:

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

= \frac{y ^{4}}{x ^{4}}

\frac{1}{( 1 + e ^{x^{n}} )}

f (x) \cdot x^{2} - 2 x - 3

c^{0.8} + 3 \cdot (- 3)^{4}

- {- 3 x^{3} - 2 x^{2} - [- x^{3} - (- 2 x - 3 x^{2})]}

(5 p - 3 a)^{3}

What is (x/y)^{-2}*(x/y)^{-3}*(x/y) ?
The solution to (x/y)^{-2}*(x/y)^{-3}*(x/y) is (y^4)/(x^4)