Calculus Examples

$3 {(\sqrt{2})}^{4} - 12 {(\sqrt{2})}^{2} + 9$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${\sqrt{2}}^{4}$ as $2^{2}$ .

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$3 {(2^{\frac{1}{2}})}^{4} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 \cdot 2^{\frac{1}{2} \cdot 4} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.3

Combine $\frac{1}{2}$ and $4$ .

$3 \cdot 2^{\frac{4}{2}} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.4

Cancel the common factor of $4$ and $2$ .

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Step 1.1.4.1

Factor $2$ out of $4$ .

$3 \cdot 2^{\frac{2 \cdot 2}{2}} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.4.2

Cancel the common factors.

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Step 1.1.4.2.1

Factor $2$ out of $2$ .

$3 \cdot 2^{\frac{2 \cdot 2}{2 (1)}} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.4.2.2

Cancel the common factor.

$3 \cdot 2^{\frac{2 \cdot 2}{2 \cdot 1}} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.4.2.3

Rewrite the expression.

$3 \cdot 2^{\frac{2}{1}} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.1.4.2.4

Divide $2$ by $1$ .

$3 \cdot 2^{2} - 12 {(\sqrt{2})}^{2} + 9$

Step 1.2

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

$3 \cdot 4 - 12 {(\sqrt{2})}^{2} + 9$

Step 1.3

Multiply $3$ by $4$ .

$12 - 12 {(\sqrt{2})}^{2} + 9$

Step 1.4

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$12 - 12 {(2^{\frac{1}{2}})}^{2} + 9$

Step 1.4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$12 - 12 \cdot 2^{\frac{1}{2} \cdot 2} + 9$

Step 1.4.3

Combine $\frac{1}{2}$ and $2$ .

$12 - 12 \cdot 2^{\frac{2}{2}} + 9$

Step 1.4.4

Cancel the common factor of $2$ .

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Step 1.4.4.1

Cancel the common factor.

$12 - 12 \cdot 2^{\frac{2}{2}} + 9$

Step 1.4.4.2

Rewrite the expression.

$12 - 12 \cdot 2^{1} + 9$

Step 1.4.5

Evaluate the exponent.

$12 - 12 \cdot 2 + 9$

Step 1.5

Multiply $- 12$ by $2$ .

$12 - 24 + 9$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $24$ from $12$ .

$- 12 + 9$

Step 2.2

Add $- 12$ and $9$ .

$- 3$