Basic Math Examples

$\sqrt[4]{63} c^{11} \cdot (\sqrt[4]{9} c^{7})$

Step 1

Rewrite using the commutative property of multiplication.

$\sqrt[4]{63} \cdot \sqrt[4]{9} c^{11} c^{7}$

Step 2

Multiply $c^{11}$ by $c^{7}$ by adding the exponents.

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Step 2.1

Move $c^{7}$ .

$\sqrt[4]{63} \cdot \sqrt[4]{9} (c^{7} c^{11})$

Step 2.2

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

$\sqrt[4]{63} \cdot \sqrt[4]{9} c^{7 + 11}$

Step 2.3

Add $7$ and $11$ .

$\sqrt[4]{63} \cdot \sqrt[4]{9} c^{18}$

Step 3

Combine using the product rule for radicals.

$\sqrt[4]{63 \cdot 9} c^{18}$

Step 4

Multiply $63$ by $9$ .

$\sqrt[4]{567} c^{18}$

Step 5

Rewrite $567$ as $3^{4} \cdot 7$ .

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Step 5.1

Factor $81$ out of $567$ .

$\sqrt[4]{81 (7)} c^{18}$

Step 5.2

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} \cdot 7} c^{18}$

Step 6

Pull terms out from under the radical.

$3 \sqrt[4]{7} c^{18}$