What is (3z)^2(6z^3)^{-3} ?

The solution to (3z)^2(6z^3)^{-3} is 1/(24z^7)

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simplify (3z)^2(6z^3)^{-3}

simplify

(3 z)^{2} (6 z^{3})^{- 3}

\frac{1}{24 z ^{7}}

Solution steps

(3 z)^{2} (6 z^{3})^{- 3}

Simplify

(3 z)^{2} : 9 z^{2}

= 9 z^{2} (6 z^{3})^{- 3}

Simplify

(6 z^{3})^{- 3} : \frac{1}{216 z ^{9}}

= 9 z^{2} \frac{1}{216 z ^{9}}

Apply the fraction rule:

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

= \frac{9 z ^{2} \cdot 1}{216 z ^{9}}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{9 z ^{2}}{216 z ^{9}}

Factor the number:

216 = 9 \cdot 24

= \frac{9 z ^{2}}{9 \cdot 24 z ^{9}}

Cancel the common factor:

9

= \frac{z ^{2}}{24 z ^{9}}

Simplify

\frac{z ^{2}}{z ^{9}} : \frac{1}{z ^{7}}

= \frac{1}{24 z ^{7}}

- 4 \cdot 15

4 (8 z - 2 t) - 3 (- t - 4 z)

(8 x)^{- 1}

(2 a^{2} b)^{0}