Algebra Examples

$x^{- 2} y^{3} \sqrt[3]{64 x^{5} y^{3}}$

Step 1

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

$\frac{1}{x^{2}} y^{3} \sqrt[3]{64 x^{5} y^{3}}$

Step 2

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

$\frac{y^{3}}{x^{2}} \sqrt[3]{64 x^{5} y^{3}}$

Step 3

Rewrite $64 x^{5} y^{3}$ as ${(4 x y)}^{3} x^{2}$ .

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Step 3.1

Rewrite $64$ as $4^{3}$ .

$\frac{y^{3}}{x^{2}} \sqrt[3]{4^{3} x^{5} y^{3}}$

Step 3.2

Factor out $x^{3}$ .

$\frac{y^{3}}{x^{2}} \sqrt[3]{4^{3} (x^{3} x^{2}) y^{3}}$

Step 3.3

Move $x^{2}$ .

$\frac{y^{3}}{x^{2}} \sqrt[3]{4^{3} x^{3} y^{3} x^{2}}$

Step 3.4

Rewrite $4^{3} (x^{3}) y^{3}$ as ${(4 x y)}^{3}$ .

$\frac{y^{3}}{x^{2}} \sqrt[3]{{(4 x y)}^{3} x^{2}}$

Step 4

Pull terms out from under the radical.

$\frac{y^{3}}{x^{2}} (4 x y \sqrt[3]{x^{2}})$

Step 5

Rewrite using the commutative property of multiplication.

$4 \frac{y^{3}}{x^{2}} (x y \sqrt[3]{x^{2}})$

Step 6

Combine $4$ and $\frac{y^{3}}{x^{2}}$ .

$\frac{4 y^{3}}{x^{2}} (x y \sqrt[3]{x^{2}})$

Step 7

Cancel the common factor of $x$ .

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Step 7.1

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

$\frac{4 y^{3}}{x \cdot x} (x y \sqrt[3]{x^{2}})$

Step 7.2

Factor $x$ out of $x y \sqrt[3]{x^{2}}$ .

$\frac{4 y^{3}}{x \cdot x} (x (y \sqrt[3]{x^{2}}))$

Step 7.3

Cancel the common factor.

$\frac{4 y^{3}}{x \cdot x} (x (y \sqrt[3]{x^{2}}))$

Step 7.4

Rewrite the expression.

$\frac{4 y^{3}}{x} (y \sqrt[3]{x^{2}})$

Step 8

Combine $y$ and $\frac{4 y^{3}}{x}$ .

$\frac{y (4 y^{3})}{x} \sqrt[3]{x^{2}}$

Step 9

Raise $y$ to the power of $1$ .

$\frac{4 (y^{1} y^{3})}{x} \sqrt[3]{x^{2}}$

Step 10

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

$\frac{4 y^{1 + 3}}{x} \sqrt[3]{x^{2}}$

Step 11

Add $1$ and $3$ .

$\frac{4 y^{4}}{x} \sqrt[3]{x^{2}}$

Step 12

Combine $\frac{4 y^{4}}{x}$ and $\sqrt[3]{x^{2}}$ .

$\frac{4 y^{4} \sqrt[3]{x^{2}}}{x}$