Algebra Examples

$\sqrt[4]{16 {(x - 3)}^{12}}$

Step 1

Rewrite $16 {(x - 3)}^{12}$ as ${(2 {(x - 3)}^{3})}^{4}$ .

$\sqrt[4]{{(2 {(x - 3)}^{3})}^{4}}$

Step 2

Pull terms out from under the radical.

$| 2 {(x - 3)}^{3} |$

Step 3

Use the Binomial Theorem.

$| 2 (x^{3} + 3 x^{2} \cdot - 3 + 3 x {(- 3)}^{2} + {(- 3)}^{3}) |$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 3$ by $3$ .

$| 2 (x^{3} - 9 x^{2} + 3 x {(- 3)}^{2} + {(- 3)}^{3}) |$

Step 4.2

Raise $- 3$ to the power of $2$ .

$| 2 (x^{3} - 9 x^{2} + 3 x \cdot 9 + {(- 3)}^{3}) |$

Step 4.3

Multiply $9$ by $3$ .

$| 2 (x^{3} - 9 x^{2} + 27 x + {(- 3)}^{3}) |$

Step 4.4

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

$| 2 (x^{3} - 9 x^{2} + 27 x - 27) |$

Step 5

Apply the distributive property.

$| 2 x^{3} + 2 (- 9 x^{2}) + 2 (27 x) + 2 \cdot - 27 |$

Step 6

Simplify.

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Step 6.1

Multiply $- 9$ by $2$ .

$| 2 x^{3} - 18 x^{2} + 2 (27 x) + 2 \cdot - 27 |$

Step 6.2

Multiply $27$ by $2$ .

$| 2 x^{3} - 18 x^{2} + 54 x + 2 \cdot - 27 |$

Step 6.3

Multiply $2$ by $- 27$ .

$| 2 x^{3} - 18 x^{2} + 54 x - 54 |$