Simplify (4b cube root of -27a^5)/(3a^2b)

$\frac{4 b \sqrt[3]{- 27 a^{5}}}{3 a^{2} b}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{4 b \sqrt[3]{- 27 a^{5}}}{3 a^{2} b}$

Rewrite the expression.

$\frac{4 \sqrt[3]{- 27 a^{5}}}{3 a^{2}}$

$\frac{4 \sqrt[3]{- 27 a^{5}}}{3 a^{2}}$

Simplify the numerator.

Rewrite $- 27 a^{5}$ as ${(- 3 a)}^{3} a^{2}$ .

Rewrite $- 27$ as ${(- 3)}^{3}$ .

$\frac{4 \sqrt[3]{{(- 3)}^{3} a^{5}}}{3 a^{2}}$

Factor out $a^{3}$ .

$\frac{4 \sqrt[3]{{(- 3)}^{3} (a^{3} a^{2})}}{3 a^{2}}$

Rewrite ${(- 3)}^{3} a^{3}$ as ${(- 3 a)}^{3}$ .

$\frac{4 \sqrt[3]{{(- 3 a)}^{3} a^{2}}}{3 a^{2}}$

$\frac{4 \sqrt[3]{{(- 3 a)}^{3} a^{2}}}{3 a^{2}}$

Pull terms out from under the radical.

$\frac{4 \cdot - 3 a \sqrt[3]{a^{2}}}{3 a^{2}}$

Multiply $4$ by $- 3$ .

$\frac{- 12 a \sqrt[3]{a^{2}}}{3 a^{2}}$

$\frac{- 12 a \sqrt[3]{a^{2}}}{3 a^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 12$ and $3$ .

Factor $3$ out of $- 12 a \sqrt[3]{a^{2}}$ .

$\frac{3 (- 4 a \sqrt[3]{a^{2}})}{3 a^{2}}$

Cancel the common factors.

Factor $3$ out of $3 a^{2}$ .

$\frac{3 (- 4 a \sqrt[3]{a^{2}})}{3 (a^{2})}$

Cancel the common factor.

$\frac{3 (- 4 a \sqrt[3]{a^{2}})}{3 a^{2}}$

Rewrite the expression.

$\frac{- 4 a \sqrt[3]{a^{2}}}{a^{2}}$

$\frac{- 4 a \sqrt[3]{a^{2}}}{a^{2}}$

$\frac{- 4 a \sqrt[3]{a^{2}}}{a^{2}}$

Cancel the common factor of $a$ and $a^{2}$ .

Factor $a$ out of $- 4 a \sqrt[3]{a^{2}}$ .

$\frac{a (- 4 \sqrt[3]{a^{2}})}{a^{2}}$

Cancel the common factors.

Factor $a$ out of $a^{2}$ .

$\frac{a (- 4 \sqrt[3]{a^{2}})}{a \cdot a}$

Cancel the common factor.

$\frac{a (- 4 \sqrt[3]{a^{2}})}{a \cdot a}$

Rewrite the expression.

$\frac{- 4 \sqrt[3]{a^{2}}}{a}$

$\frac{- 4 \sqrt[3]{a^{2}}}{a}$

$\frac{- 4 \sqrt[3]{a^{2}}}{a}$

Move the negative in front of the fraction.

$- \frac{4 \sqrt[3]{a^{2}}}{a}$

$- \frac{4 \sqrt[3]{a^{2}}}{a}$

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