Simplify 3x^3 square root of x^8y+x^2 cube root of x^5y

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

Step 1

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

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

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

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 ${(x^{2})}^{2}$ .

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

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

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.

Move $x^{4}$ .

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

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

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

Add $4$ and $3$ .

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

Step 5

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

Factor out $x^{3}$ .

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

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.

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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