Simplify 3x^(8/3)y^-2 cube root of 8xy^3

$3 x^{\frac{8}{3}} y^{- 2} \sqrt[3]{8 x y^{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 x^{\frac{8}{3}} \frac{1}{y^{2}} \sqrt[3]{8 x y^{3}}$

Step 2

Multiply $3 x^{\frac{8}{3}} \frac{1}{y^{2}}$ .

Combine $3$ and $\frac{1}{y^{2}}$ .

$x^{\frac{8}{3}} \frac{3}{y^{2}} \sqrt[3]{8 x y^{3}}$

Combine $x^{\frac{8}{3}}$ and $\frac{3}{y^{2}}$ .

$\frac{x^{\frac{8}{3}} \cdot 3}{y^{2}} \sqrt[3]{8 x y^{3}}$

Step 3

Move $3$ to the left of $x^{\frac{8}{3}}$ .

$\frac{3 \cdot x^{\frac{8}{3}}}{y^{2}} \sqrt[3]{8 x y^{3}}$

Step 4

Rewrite $8 x y^{3}$ as ${(2 y)}^{3} x$ .

Rewrite $8$ as $2^{3}$ .

$\frac{3 x^{\frac{8}{3}}}{y^{2}} \sqrt[3]{2^{3} x y^{3}}$

Move $x$ .

$\frac{3 x^{\frac{8}{3}}}{y^{2}} \sqrt[3]{2^{3} y^{3} x}$

Rewrite $2^{3} y^{3}$ as ${(2 y)}^{3}$ .

$\frac{3 x^{\frac{8}{3}}}{y^{2}} \sqrt[3]{{(2 y)}^{3} x}$

Step 5

Pull terms out from under the radical.

$\frac{3 x^{\frac{8}{3}}}{y^{2}} (2 y \sqrt[3]{x})$

Step 6

Rewrite using the commutative property of multiplication.

$2 \frac{3 x^{\frac{8}{3}}}{y^{2}} (y \sqrt[3]{x})$

Step 7

Multiply $2 \frac{3 x^{\frac{8}{3}}}{y^{2}}$ .

Combine $2$ and $\frac{3 x^{\frac{8}{3}}}{y^{2}}$ .

$\frac{2 (3 x^{\frac{8}{3}})}{y^{2}} (y \sqrt[3]{x})$

Multiply $3$ by $2$ .

$\frac{6 x^{\frac{8}{3}}}{y^{2}} (y \sqrt[3]{x})$

Step 8

Cancel the common factor of $y$ .

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

$\frac{6 x^{\frac{8}{3}}}{y \cdot y} (y \sqrt[3]{x})$

Factor $y$ out of $y \sqrt[3]{x}$ .

$\frac{6 x^{\frac{8}{3}}}{y \cdot y} (y (\sqrt[3]{x}))$

Cancel the common factor.

$\frac{6 x^{\frac{8}{3}}}{y \cdot y} (y \sqrt[3]{x})$

Rewrite the expression.

$\frac{6 x^{\frac{8}{3}}}{y} \sqrt[3]{x}$

Step 9

Combine $\frac{6 x^{\frac{8}{3}}}{y}$ and $\sqrt[3]{x}$ .

$\frac{6 x^{\frac{8}{3}} \sqrt[3]{x}}{y}$

Step 10

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$\frac{6 (x^{\frac{1}{3}} x^{\frac{8}{3}})}{y}$

Step 11

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 x^{\frac{1}{3} + \frac{8}{3}}}{y}$

Step 12

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{6 x^{\frac{1 + 8}{3}}}{y}$

Add $1$ and $8$ .

$\frac{6 x^{\frac{9}{3}}}{y}$

Step 13

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9$ .

$\frac{6 x^{\frac{3 \cdot 3}{3}}}{y}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{6 x^{\frac{3 \cdot 3}{3 (1)}}}{y}$

Cancel the common factor.

$\frac{6 x^{\frac{3 \cdot 3}{3 \cdot 1}}}{y}$

Rewrite the expression.

$\frac{6 x^{\frac{3}{1}}}{y}$

Divide $3$ by $1$ .

$\frac{6 x^{3}}{y}$

Simplify 3x^(8/3)y^-2 cube root of 8xy^3

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