Simplify ( cube root of u^4)( cube root of 2u^8)

$(\sqrt[3]{u^{4}}) (\sqrt[3]{2 u^{8}})$

Step 1

Factor out $u^{3}$ .

$\sqrt[3]{u^{3} u} \sqrt[3]{2 u^{8}}$

Step 2

Pull terms out from under the radical.

$u \sqrt[3]{u} \sqrt[3]{2 u^{8}}$

Step 3

Rewrite $2 u^{8}$ as ${(u^{2})}^{3} \cdot (2 u^{2})$ .

Factor out $u^{6}$ .

$u \sqrt[3]{u} \sqrt[3]{2 (u^{6} u^{2})}$

Rewrite $u^{6}$ as ${(u^{2})}^{3}$ .

$u \sqrt[3]{u} \sqrt[3]{2 ({(u^{2})}^{3} u^{2})}$

Reorder $2$ and ${(u^{2})}^{3}$ .

$u \sqrt[3]{u} \sqrt[3]{{(u^{2})}^{3} \cdot 2 u^{2}}$

Add parentheses.

$u \sqrt[3]{u} \sqrt[3]{{(u^{2})}^{3} \cdot (2 u^{2})}$

Step 4

Pull terms out from under the radical.

$u \sqrt[3]{u} (u^{2} \sqrt[3]{2 u^{2}})$

Step 5

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

Move $u^{2}$ .

$u^{2} u \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

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

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

$u^{2} u^{1} \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

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

$u^{2 + 1} \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

Add $2$ and $1$ .

$u^{3} \sqrt[3]{u} \sqrt[3]{2 u^{2}}$

Step 6

Multiply $u^{3} \sqrt[3]{u} \sqrt[3]{2 u^{2}}$ .

Combine using the product rule for radicals.

$u^{3} \sqrt[3]{2 u^{2} u}$

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

$u^{3} \sqrt[3]{2 (u^{1} u^{2})}$

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

$u^{3} \sqrt[3]{2 u^{1 + 2}}$

Add $1$ and $2$ .

$u^{3} \sqrt[3]{2 u^{3}}$

Step 7

Reorder $2$ and $u^{3}$ .

$u^{3} \sqrt[3]{u^{3} \cdot 2}$

Step 8

Pull terms out from under the radical.

$u^{3} (u \sqrt[3]{2})$

Step 9

Rewrite using the commutative property of multiplication.

$\sqrt[3]{2} u^{3} u$

Step 10

Multiply $u^{3}$ by $u$ by adding the exponents.

Move $u$ .

$\sqrt[3]{2} (u \cdot u^{3})$

Multiply $u$ by $u^{3}$ .

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

$\sqrt[3]{2} (u^{1} u^{3})$

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

$\sqrt[3]{2} u^{1 + 3}$

Add $1$ and $3$ .

$\sqrt[3]{2} u^{4}$

Simplify ( cube root of u^4)( cube root of 2u^8)

Related Questions

Support LCMGCF.com by disabling your adblocker.