What is ((-4x^5y^3z^7)^3(-3x^2yz^4)^2)/((-2x^3y^4z^2)^4) ?

The solution to ((-4x^5y^3z^7)^3(-3x^2yz^4)^2)/((-2x^3y^4z^2)^4) is -(36x^7z^{21})/(y^5)

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simplify ((-4x^5y^3z^7)^3(-3x^2yz^4)^2)/((-2x^3y^4z^2)^4)

simplify

\frac{( - 4 x ^{5} y ^{3} z ^{7} ) ^{3} ( - 3 x ^{2} y z ^{4} ) ^{2}}{( - 2 x ^{3} y ^{4} z ^{2} ) ^{4}}

- \frac{36 x ^{7} z ^{21}}{y ^{5}}

Solution steps

\frac{( - 4 x ^{5} y ^{3} z ^{7} ) ^{3} ( - 3 x ^{2} y z ^{4} ) ^{2}}{( - 2 x ^{3} y ^{4} z ^{2} ) ^{4}}

Simplify

(- 2 x^{3} y^{4} z^{2})^{4} : 16 x^{12} y^{16} z^{8}

= \frac{( - 4 x ^{5} y ^{3} z ^{7} ) ^{3} ( - 3 x ^{2} y z ^{4} ) ^{2}}{16 x ^{12} y ^{16} z ^{8}}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 4 x^{5} y^{3} z^{7})^{3} = - (4 x^{5} y^{3} z^{7})^{3}

= \frac{- ( 4 x ^{5} y ^{3} z ^{7} ) ^{3} ( - 3 x ^{2} y z ^{4} ) ^{2}}{16 x ^{12} y ^{16} z ^{8}}

Simplify

(4 x^{5} y^{3} z^{7})^{3} : 4^{3} x^{15} y^{9} z^{21}

= \frac{- 4 ^{3} x ^{15} y ^{9} z ^{21} ( - 3 x ^{2} y z ^{4} ) ^{2}}{16 x ^{12} y ^{16} z ^{8}}

Factor the number:

16 = 4^{2}

= \frac{- 4 ^{3} x ^{15} y ^{9} z ^{21} ( - 3 x ^{2} y z ^{4} ) ^{2}}{4 ^{2} x ^{12} y ^{16} z ^{8}}

\frac{4 ^{3}}{4 ^{2}} = 4

= \frac{- 4 x ^{15} y ^{9} z ^{21} ( - 3 x ^{2} y z ^{4} ) ^{2}}{x ^{12} y ^{16} z ^{8}}

Simplify

\frac{x ^{15}}{x ^{12}} : x^{3}

= \frac{- 4 x ^{3} y ^{9} z ^{21} ( - 3 x ^{2} y z ^{4} ) ^{2}}{y ^{16} z ^{8}}

Simplify

\frac{z ^{21}}{z ^{8}} : z^{13}

= \frac{- 4 x ^{3} y ^{9} z ^{13} ( - 3 x ^{2} y z ^{4} ) ^{2}}{y ^{16}}

Simplify

\frac{y ^{9}}{y ^{16}} : \frac{1}{y ^{7}}

= \frac{- 4 x ^{3} z ^{13} ( - 3 x ^{2} y z ^{4} ) ^{2}}{y ^{7}}

Simplify

\frac{- 4 x ^{3} z ^{13} ( - 3 x ^{2} y z ^{4} ) ^{2}}{y ^{7}} : - \frac{36 x ^{7} z ^{21}}{y ^{5}}

= - \frac{36 x ^{7} z ^{21}}{y ^{5}}

- x^{3} + 6 x^{2}

\frac{\frac{a}{b}}{\frac{c}{d}}

\frac{1}{4} (6) + 3 (7)

(\frac{1}{25 x} \cdot x^{9})^{- \frac{1}{2}}

9 (\frac{8 + 6}{9}) - 6

What is ((-4x^5y^3z^7)^3(-3x^2yz^4)^2)/((-2x^3y^4z^2)^4) ?
The solution to ((-4x^5y^3z^7)^3(-3x^2yz^4)^2)/((-2x^3y^4z^2)^4) is -(36x^7z^{21})/(y^5)