What is (((-81x^3*y^4))/((27x*y^3)))^3 ?

The solution to (((-81x^3*y^4))/((27x*y^3)))^3 is -27x^6y^3

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simplify (((-81x^3y^4))/((27xy^3)))^3

simplify

(\frac{( - 81 x ^{3} \cdot y ^{4} )}{( 27 x \cdot y ^{3} )})^{3}

- 27 x^{6} y^{3}

Solution steps

(\frac{- 81 x ^{3} y ^{4}}{27 x y ^{3}})^{3}

Apply exponent rule:

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

= \frac{( - 81 x ^{3} y ^{4} ) ^{3}}{( 27 x y ^{3} ) ^{3}}

Simplify

(- 81 x^{3} y^{4})^{3} : - 531441 x^{9} y^{12}

= \frac{- 531441 x ^{9} y ^{12}}{( 27 x y ^{3} ) ^{3}}

Simplify

(27 x y^{3})^{3} : 19683 x^{3} y^{9}

= \frac{- 531441 x ^{9} y ^{12}}{19683 x ^{3} y ^{9}}

Apply the fraction rule:

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

= - \frac{531441 x ^{9} y ^{12}}{19683 x ^{3} y ^{9}}

Divide the numbers:

\frac{531441}{19683} = 27

= \frac{27 x ^{9} y ^{12}}{x ^{3} y ^{9}}

Apply exponent rule:

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

\frac{x ^{9}}{x ^{3}} = x^{9 - 3}

= \frac{27 y ^{12} x ^{9 - 3}}{y ^{9}}

Subtract the numbers:

9 - 3 = 6

= \frac{27 x ^{6} y ^{12}}{y ^{9}}

Apply exponent rule:

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

\frac{y ^{12}}{y ^{9}} = y^{12 - 9}

= 27 x^{6} y^{12 - 9}

Subtract the numbers:

12 - 9 = 3

= - 27 x^{6} y^{3}

(i) x^{3} + 13 x^{2} + 32 x + 20

16 \cdot (x - y)^{3} - 24 \cdot (x - y)^{2}

a^{4} - 6 a^{2} + 25

25 y^{4} + 120 y^{2} + 144

- 4 x (x + 3) (x - 4) - 3 x (x^{2} - x + 1)

What is (((-81x^3*y^4))/((27x*y^3)))^3 ?
The solution to (((-81x^3*y^4))/((27x*y^3)))^3 is -27x^6y^3