Basic Math Examples

$(\sqrt[4]{a b^{2}}) \cdot (\sqrt[4]{27 a b})$

Step 1

Multiply $(\sqrt[4]{a b^{2}}) (\sqrt[4]{27 a b})$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt[4]{a b^{2} (27 a b)}$

Step 1.2

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

$\sqrt[4]{a^{1} a b^{2} (27 b)}$

Step 1.3

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

$\sqrt[4]{a^{1} a^{1} b^{2} (27 b)}$

Step 1.4

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

$\sqrt[4]{a^{1 + 1} b^{2} (27 b)}$

Step 1.5

Add $1$ and $1$ .

$\sqrt[4]{a^{2} b^{2} (27 b)}$

Step 1.6

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

$\sqrt[4]{a^{2} (27 (b^{2} b^{1}))}$

Step 1.7

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

$\sqrt[4]{a^{2} (27 b^{2 + 1})}$

Step 1.8

Add $2$ and $1$ .

$\sqrt[4]{a^{2} (27 b^{3})}$

Step 2

Reorder factors in $\sqrt[4]{a^{2} \cdot 27 b^{3}}$ .

$\sqrt[4]{27 a^{2} b^{3}}$