Trigonometry Examples

${(\sqrt[n]{a})}^{n} = a$

Step 1

Rewrite ${\sqrt[n]{a}}^{n}$ as $a$ .

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Step 1.1

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

${(a^{\frac{1}{n}})}^{n} = a$

Step 1.2

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

$a^{\frac{1}{n} n} = a$

Step 1.3

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

$a^{\frac{n}{n}} = a$

Step 1.4

Cancel the common factor of $n$ .

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Step 1.4.1

Cancel the common factor.

$a^{\frac{n}{n}} = a$

Step 1.4.2

Rewrite the expression.

$a^{1} = a$

Step 1.5

Simplify.

$a = a$

Step 2

Since the two sides have been shown to be equivalent, the equation is an identity.

${(\sqrt[n]{a})}^{n} = a$ is an identity.