What is (3x^{-4}yz^{-7})(3x)^{-3} ?

The solution to (3x^{-4}yz^{-7})(3x)^{-3} is y/(9x^7z^7)

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simplify (3x^{-4}yz^{-7})(3x)^{-3}

simplify

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

\frac{y}{9 x ^{7} z ^{7}}

Solution steps

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

Simplify

3 x^{- 4} y z^{- 7} : \frac{3 y}{x ^{4} z ^{7}}

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

Simplify

(3 x)^{- 3} : \frac{1}{27 x ^{3}}

= \frac{3 y}{x ^{4} z ^{7}} \cdot \frac{1}{27 x ^{3}}

Apply the fraction rule:

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

= \frac{3 y \cdot 1}{x ^{4} z ^{7} \cdot 27 x ^{3}}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{3 y}{x ^{4} z ^{7} \cdot 27 x ^{3}}

Factor the number:

27 = 3 \cdot 9

= \frac{3 y}{x ^{4} z ^{7} \cdot 3 \cdot 9 x ^{3}}

Cancel the common factor:

3

= \frac{y}{x ^{4} z ^{7} \cdot 9 x ^{3}}

Simplify

x^{4} x^{3} : x^{7}

= \frac{y}{x ^{7} z ^{7} \cdot 9}

= \frac{y}{9 x ^{7} z ^{7}}

4 x^{2} + 64 x

x + x + x + x + x

- \frac{4}{5} + \frac{3}{5}

x^{2} y 81 x^{12} y^{8}

\frac{4}{9} (2 n - 3)

What is (3x^{-4}yz^{-7})(3x)^{-3} ?
The solution to (3x^{-4}yz^{-7})(3x)^{-3} is y/(9x^7z^7)