What is (xy^2z^3)^{-1}(xyz)^3 ?

The solution to (xy^2z^3)^{-1}(xyz)^3 is x^2y

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simplify (xy^2z^3)^{-1}(xyz)^3

simplify

(x y^{2} z^{3})^{- 1} (x yz)^{3}

x^{2} y

Solution steps

(x y^{2} z^{3})^{- 1} (x yz)^{3}

Apply exponent rule:

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

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

= \frac{1}{x y ^{2} z ^{3}} (x yz)^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(x yz)^{3} = x^{3} y^{3} z^{3}

= \frac{1}{x y ^{2} z ^{3}} x^{3} y^{3} z^{3}

Apply the fraction rule:

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

= \frac{1 \cdot x ^{3} y ^{3} z ^{3}}{x y ^{2} z ^{3}}

Apply rule:

1 \cdot a = a

1 \cdot x^{3} y^{3} z^{3} = x^{3} y^{3} z^{3}

= \frac{x ^{3} y ^{3} z ^{3}}{x y ^{2} z ^{3}}

Cancel the common factor:

z^{3}

= \frac{x ^{3} y ^{3}}{x y ^{2}}

Simplify

\frac{x ^{3}}{x} : x^{2}

= \frac{x ^{2} y ^{3}}{y ^{2}}

Simplify

\frac{y ^{3}}{y ^{2}} : y

= x^{2} y

(\frac{5}{9})^{- 2}

5 + \frac{1}{7} b = - 2

275

t^{2} + 3 t - 1 = 0

\frac{2}{3} + \frac{2}{6}