Finite Math Examples

$\sqrt[3]{{(x + 6)}^{12}}$

Step 1

Rewrite ${(x + 6)}^{12}$ as ${({(x + 6)}^{4})}^{3}$ .

$\sqrt[3]{{({(x + 6)}^{4})}^{3}}$

Step 2

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

${(x + 6)}^{4}$

Step 3

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot 6 + 6 x^{2} \cdot 6^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4

Simplify each term.

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Step 4.1

Multiply $6$ by $4$ .

$x^{4} + 24 x^{3} + 6 x^{2} \cdot 6^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4.2

Multiply $6$ by $6^{2}$ by adding the exponents.

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Step 4.2.1

Move $6^{2}$ .

$x^{4} + 24 x^{3} + 6^{2} \cdot 6 x^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4.2.2

Multiply $6^{2}$ by $6$ .

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Step 4.2.2.1

Raise $6$ to the power of $1$ .

$x^{4} + 24 x^{3} + 6^{2} \cdot 6^{1} x^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4.2.2.2

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

$x^{4} + 24 x^{3} + 6^{2 + 1} x^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4.2.3

Add $2$ and $1$ .

$x^{4} + 24 x^{3} + 6^{3} x^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4.3

Raise $6$ to the power of $3$ .

$x^{4} + 24 x^{3} + 216 x^{2} + 4 x \cdot 6^{3} + 6^{4}$

Step 4.4

Raise $6$ to the power of $3$ .

$x^{4} + 24 x^{3} + 216 x^{2} + 4 x \cdot 216 + 6^{4}$

Step 4.5

Multiply $216$ by $4$ .

$x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 6^{4}$

Step 4.6

Raise $6$ to the power of $4$ .

$x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296$