Trigonometry Examples

${(\sqrt{2})}^{2014}$

Step 1

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

${(2^{\frac{1}{2}})}^{2014}$

Step 2

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

$2^{\frac{1}{2} \cdot 2014}$

Step 3

Combine $\frac{1}{2}$ and $2014$ .

$2^{\frac{2014}{2}}$

Step 4

Cancel the common factor of $2014$ and $2$ .

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Step 4.1

Factor $2$ out of $2014$ .

$2^{\frac{2 \cdot 1007}{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2$ .

$2^{\frac{2 \cdot 1007}{2 (1)}}$

Step 4.2.2

Cancel the common factor.

$2^{\frac{2 \cdot 1007}{2 \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$2^{\frac{1007}{1}}$

Step 4.2.4

Divide $1007$ by $1$ .

$2^{1007}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$2^{1007}$

Decimal Form:

$1.37153101 \cdot 10^{303}$