Algebra Examples

$3 x^{3} \sqrt{x^{8} y} + x^{2} \sqrt[3]{x^{5} y}$

Step 1

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

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Step 1.1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$3 x^{3} \sqrt{{(x^{4})}^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Step 1.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$3 x^{3} \sqrt{{({(x^{2})}^{2})}^{2} y} + x^{2} \sqrt[3]{x^{5} y}$

Step 2

Pull terms out from under the radical.

$3 x^{3} ({(x^{2})}^{2} \sqrt{y}) + x^{2} \sqrt[3]{x^{5} y}$

Step 3

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 x^{3} (x^{2 \cdot 2} \sqrt{y}) + x^{2} \sqrt[3]{x^{5} y}$

Step 3.2

Multiply $2$ by $2$ .

$3 x^{3} (x^{4} \sqrt{y}) + x^{2} \sqrt[3]{x^{5} y}$

Step 4

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

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Step 4.1

Move $x^{4}$ .

$3 (x^{4} x^{3}) \sqrt{y} + x^{2} \sqrt[3]{x^{5} y}$

Step 4.2

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

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

Step 4.3

Add $4$ and $3$ .

$3 x^{7} \sqrt{y} + x^{2} \sqrt[3]{x^{5} y}$

Step 5

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

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Step 5.1

Factor out $x^{3}$ .

$3 x^{7} \sqrt{y} + x^{2} \sqrt[3]{x^{3} x^{2} y}$

Step 5.2

Add parentheses.

$3 x^{7} \sqrt{y} + x^{2} \sqrt[3]{x^{3} (x^{2} y)}$

Step 6

Pull terms out from under the radical.

$3 x^{7} \sqrt{y} + x^{2} (x \sqrt[3]{x^{2} y})$

Step 7

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 7.1

Move $x$ .

$3 x^{7} \sqrt{y} + x \cdot x^{2} \sqrt[3]{x^{2} y}$

Step 7.2

Multiply $x$ by $x^{2}$ .

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Step 7.2.1

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

$3 x^{7} \sqrt{y} + x^{1} x^{2} \sqrt[3]{x^{2} y}$

Step 7.2.2

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

$3 x^{7} \sqrt{y} + x^{1 + 2} \sqrt[3]{x^{2} y}$

Step 7.3

Add $1$ and $2$ .

$3 x^{7} \sqrt{y} + x^{3} \sqrt[3]{x^{2} y}$