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

The solution to ((-(x^2*y^4))/((x*y^{-2))})^3 is -x^3y^{18}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((-(x^2y^4))/((xy^{-2))})^3

simplify

(\frac{- ( x ^{2} \cdot y ^{4} )}{( x \cdot y ^{- 2} )})^{3}

- x^{3} y^{18}

Solution steps

(\frac{- ( x ^{2} y ^{4} )}{x y ^{- 2}})^{3}

Apply rule:

- (a) = - a

- (x^{2} y^{4}) = - x^{2} y^{4}

= (\frac{- x ^{2} y ^{4}}{x y ^{- 2}})^{3}

Apply exponent rule:

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

= \frac{( - x ^{2} y ^{4} ) ^{3}}{( x y ^{- 2} ) ^{3}}

Simplify

(- x^{2} y^{4})^{3} : - x^{6} y^{12}

= \frac{- x ^{6} y ^{12}}{( x y ^{- 2} ) ^{3}}

Simplify

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

= \frac{- x ^{6} y ^{12}}{\frac{x ^{3}}{y ^{6}}}

Apply the fraction rule:

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

= - \frac{x ^{6} y ^{12}}{\frac{x ^{3}}{y ^{6}}}

Apply the fraction rule:

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

\frac{x ^{6} y ^{12}}{\frac{x ^{3}}{y ^{6}}} = \frac{x ^{6} y ^{12} y ^{6}}{x ^{3}}

= - \frac{x ^{6} y ^{12} y ^{6}}{x ^{3}}

Apply exponent rule:

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

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

= y^{12} y^{6} x^{6 - 3}

Subtract the numbers:

6 - 3 = 3

= - x^{3} y^{12} y^{6}

Apply exponent rule:

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

y^{12} y^{6} = y^{12 + 6}

= - x^{3} y^{12 + 6}

Add the numbers:

12 + 6 = 18

= - x^{3} y^{18}

(2 a + b)^{3} - (a + 3 b)^{3}

\frac{1}{16} \cdot x^{2} \cdot y^{6} + \frac{1}{6} \cdot x \cdot y^{3} + \frac{1}{9}

8 a^{3} + y^{3}

34568 \frac{( sec ( a ) )}{( tan ( a ) + cot ( a ) )}

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

What is ((-(x^2*y^4))/((x*y^{-2))})^3 ?
The solution to ((-(x^2*y^4))/((x*y^{-2))})^3 is -x^3y^{18}