Algebra Examples

$\sqrt[5]{a^{3} b^{2}} \cdot \sqrt[5]{b^{3} c^{4}} \cdot \sqrt[5]{a^{2} c}$

Step 1

Multiply $\sqrt[5]{a^{3} b^{2}} \sqrt[5]{b^{3} c^{4}}$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt[5]{a^{3} b^{2} (b^{3} c^{4})} \cdot \sqrt[5]{a^{2} c}$

Step 1.2

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

$\sqrt[5]{a^{3} b^{3 + 2} c^{4}} \cdot \sqrt[5]{a^{2} c}$

Step 1.3

Add $3$ and $2$ .

$\sqrt[5]{a^{3} b^{5} c^{4}} \cdot \sqrt[5]{a^{2} c}$

Step 2

Rewrite $a^{3} b^{5} c^{4}$ as $b^{5} (a^{3} c^{4})$ .

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Step 2.1

Reorder $a^{3}$ and $b^{5}$ .

$\sqrt[5]{b^{5} a^{3} c^{4}} \cdot \sqrt[5]{a^{2} c}$

Step 2.2

Add parentheses.

$\sqrt[5]{b^{5} (a^{3} c^{4})} \cdot \sqrt[5]{a^{2} c}$

Step 3

Pull terms out from under the radical.

$b \sqrt[5]{a^{3} c^{4}} \cdot \sqrt[5]{a^{2} c}$

Step 4

Multiply $b \sqrt[5]{a^{3} c^{4}} \sqrt[5]{a^{2} c}$ .

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Step 4.1

Combine using the product rule for radicals.

$b \sqrt[5]{a^{2} c (a^{3} c^{4})}$

Step 4.2

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

$b \sqrt[5]{a^{3 + 2} c \cdot c^{4}}$

Step 4.3

Add $3$ and $2$ .

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

Step 4.4

Multiply $c$ by $c^{4}$ by adding the exponents.

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Step 4.4.1

Move $c^{4}$ .

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

Step 4.4.2

Multiply $c^{4}$ by $c$ .

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Step 4.4.2.1

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

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

Step 4.4.2.2

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

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

Step 4.4.3

Add $4$ and $1$ .

$b \sqrt[5]{a^{5} c^{5}}$

Step 5

Rewrite $a^{5} c^{5}$ as ${(a c)}^{5}$ .

$b \sqrt[5]{{(a c)}^{5}}$

Step 6

Pull terms out from under the radical, assuming real numbers.

$b a c$