Simplify the Radical Expression fourth root of 8a^3b* fourth root of 10a^2b^7

$\sqrt[4]{8 a^{3} b} \cdot \sqrt[4]{10 a^{2} b^{7}}$

Rewrite $10 a^{2} b^{7}$ as $b^{4} \cdot (10 a^{2} b^{3})$ .

Factor out $b^{4}$ .

$\sqrt[4]{8 a^{3} b} \cdot \sqrt[4]{10 a^{2} (b^{4} b^{3})}$

Move $a^{2}$ .

$\sqrt[4]{8 a^{3} b} \cdot \sqrt[4]{10 b^{4} a^{2} b^{3}}$

Reorder $10$ and $b^{4}$ .

$\sqrt[4]{8 a^{3} b} \cdot \sqrt[4]{b^{4} \cdot 10 a^{2} b^{3}}$

Add parentheses.

$\sqrt[4]{8 a^{3} b} \cdot \sqrt[4]{b^{4} \cdot 10 (a^{2} b^{3})}$

Add parentheses.

$\sqrt[4]{8 a^{3} b} \cdot \sqrt[4]{b^{4} \cdot (10 a^{2} b^{3})}$

Pull terms out from under the radical.

$\sqrt[4]{8 a^{3} b} \cdot (| b | \sqrt[4]{10 a^{2} b^{3}})$

Multiply $\sqrt[4]{8 a^{3} b} (| b | \sqrt[4]{10 a^{2} b^{3}})$ .

Combine using the product rule for radicals.

$\sqrt[4]{10 a^{2} b^{3} (8 a^{3} b)} | b |$

Multiply $8$ by $10$ .

$\sqrt[4]{80 a^{2} b^{3} (a^{3} b)} | b |$

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

$\sqrt[4]{80 a^{3 + 2} b^{3} b} | b |$

Add $3$ and $2$ .

$\sqrt[4]{80 a^{5} b^{3} b} | b |$

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

$\sqrt[4]{80 a^{5} (b^{1} b^{3})} | b |$

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

$\sqrt[4]{80 a^{5} b^{1 + 3}} | b |$

Add $1$ and $3$ .

$\sqrt[4]{80 a^{5} b^{4}} | b |$

Rewrite $80 a^{5} b^{4}$ as ${(2 a b)}^{4} \cdot (5 a)$ .

Factor $16$ out of $80$ .

$\sqrt[4]{16 (5) a^{5} b^{4}} | b |$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 5 a^{5} b^{4}} | b |$

Factor out $a^{4}$ .

$\sqrt[4]{2^{4} \cdot 5 (a^{4} a) b^{4}} | b |$

Move $a$ .

$\sqrt[4]{2^{4} \cdot 5 (a^{4}) b^{4} a} | b |$

Move $5$ .

$\sqrt[4]{(2^{4} (a^{4})) b^{4} \cdot 5 a} | b |$

Rewrite $(2^{4} (a^{4})) b^{4}$ as ${(2 a b)}^{4}$ .

$\sqrt[4]{{(2 a b)}^{4} \cdot 5 a} | b |$

Add parentheses.

$\sqrt[4]{{(2 a b)}^{4} \cdot (5 a)} | b |$

Pull terms out from under the radical.

$| 2 a b | \sqrt[4]{5 a} | b |$

Remove non-negative terms from the absolute value.

$2 | a b | \sqrt[4]{5 a} | b |$

Multiply $2 | a b | \sqrt[4]{5 a} | b |$ .

To multiply absolute values, multiply the terms inside each absolute value.

$2 | b (a b) | \sqrt[4]{5 a}$

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

$2 | a (b^{1} b) | \sqrt[4]{5 a}$

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

$2 | a (b^{1} b^{1}) | \sqrt[4]{5 a}$

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

$2 | a b^{1 + 1} | \sqrt[4]{5 a}$

Add $1$ and $1$ .

$2 | a b^{2} | \sqrt[4]{5 a}$

Remove non-negative terms from the absolute value.

$2 b^{2} | a | \sqrt[4]{5 a}$

Simplify the Radical Expression fourth root of 8a^3b* fourth root of 10a^2b^7

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