What is ((4xy)/(5x^2y^{-2)})^2 ?

The solution to ((4xy)/(5x^2y^{-2)})^2 is (16y^6)/(25x^2)

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simplify ((4xy)/(5x^2y^{-2)})^2

simplify

(\frac{4 x y}{5 x ^{2} y ^{- 2}})^{2}

\frac{16 y ^{6}}{25 x ^{2}}

Solution steps

(\frac{4 x y}{5 x ^{2} y ^{- 2}})^{2}

Apply exponent rule:

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

= \frac{( 4 x y ) ^{2}}{( 5 x ^{2} y ^{- 2} ) ^{2}}

Simplify

(4 x y)^{2} : 16 x^{2} y^{2}

= \frac{16 x ^{2} y ^{2}}{( 5 x ^{2} y ^{- 2} ) ^{2}}

Simplify

(5 x^{2} y^{- 2})^{2} : \frac{25 x ^{4}}{y ^{4}}

= \frac{16 x ^{2} y ^{2}}{\frac{25 x ^{4}}{y ^{4}}}

Apply the fraction rule:

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

= \frac{16 x ^{2} y ^{2} y ^{4}}{25 x ^{4}}

Apply exponent rule:

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

\frac{x ^{2}}{x ^{4}} = \frac{1}{x ^{4 - 2}}

= \frac{16 y ^{4} y ^{2}}{25 x ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

= \frac{16 y ^{4} y ^{2}}{25 x ^{2}}

16 y^{4} y^{2} = 16 y^{6}

= \frac{16 y ^{6}}{25 x ^{2}}

36 - 4.9 (x)^{2} = 10

(\frac{2}{7})^{2}

- 6 \leq \frac{2 x + 11}{7} < 2

(\frac{x ^{2}}{y ^{3}})^{5}

(x + 2) (x - 2)

What is ((4xy)/(5x^2y^{-2)})^2 ?
The solution to ((4xy)/(5x^2y^{-2)})^2 is (16y^6)/(25x^2)