Trigonometry Examples

$3 \sqrt{10 x^{4 \sqrt{10}}}$

Step 1

Rewrite $10 x^{4 \sqrt{10}}$ as ${({(x^{\sqrt{10}})}^{2})}^{2} \cdot 10$ .

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Step 1.1

Rewrite $x^{4 \sqrt{10}}$ as ${(x^{2 \sqrt{10}})}^{2}$ .

$3 \sqrt{10 {(x^{2 \sqrt{10}})}^{2}}$

Step 1.2

Reorder $10$ and ${(x^{2 \sqrt{10}})}^{2}$ .

$3 \sqrt{{(x^{2 \sqrt{10}})}^{2} \cdot 10}$

Step 1.3

Rewrite $x^{2 \sqrt{10}}$ as ${(x^{\sqrt{10}})}^{2}$ .

$3 \sqrt{{({(x^{\sqrt{10}})}^{2})}^{2} \cdot 10}$

Step 2

Pull terms out from under the radical.

$3 ({(x^{\sqrt{10}})}^{2} \sqrt{10})$

Step 3

Multiply the exponents in ${(x^{\sqrt{10}})}^{2}$ .

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Step 3.1

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

$3 (x^{\sqrt{10} \cdot 2} \sqrt{10})$

Step 3.2

Move $2$ to the left of $\sqrt{10}$ .

$3 (x^{2 \sqrt{10}} \sqrt{10})$

$3 x^{2 \sqrt{10}} \sqrt{10}$