Basic Math Examples

$y = 2 {(\frac{{(- 1)}^{\frac{1}{10}}}{4^{\frac{3}{10}}})}^{\frac{2}{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $- 1$ as $i^{10}$ .

$y = 2 {(\frac{{(i^{10})}^{\frac{1}{10}}}{4^{\frac{3}{10}}})}^{\frac{2}{3}}$

Step 1.2

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

$y = 2 {(\frac{i^{10 (\frac{1}{10})}}{4^{\frac{3}{10}}})}^{\frac{2}{3}}$

Step 1.3

Cancel the common factor of $10$ .

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Step 1.3.1

Cancel the common factor.

$y = 2 {(\frac{i^{10 (\frac{1}{10})}}{4^{\frac{3}{10}}})}^{\frac{2}{3}}$

Step 1.3.2

Rewrite the expression.

$y = 2 {(\frac{i^{1}}{4^{\frac{3}{10}}})}^{\frac{2}{3}}$

Step 1.4

Simplify.

$y = 2 {(\frac{i}{4^{\frac{3}{10}}})}^{\frac{2}{3}}$

Step 2

Combine fractions.

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Step 2.1

Apply the product rule to $\frac{i}{4^{\frac{3}{10}}}$ .

$y = 2 \frac{i^{\frac{2}{3}}}{{(4^{\frac{3}{10}})}^{\frac{2}{3}}}$

Step 2.2

Multiply the exponents in ${(4^{\frac{3}{10}})}^{\frac{2}{3}}$ .

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Step 2.2.1

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

$y = 2 \frac{i^{\frac{2}{3}}}{4^{\frac{3}{10} \cdot \frac{2}{3}}}$

Step 2.2.2

Cancel the common factor of $3$ .

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Step 2.2.2.1

Cancel the common factor.

$y = 2 \frac{i^{\frac{2}{3}}}{4^{\frac{3}{10} \cdot \frac{2}{3}}}$

Step 2.2.2.2

Rewrite the expression.

$y = 2 \frac{i^{\frac{2}{3}}}{4^{\frac{1}{10} \cdot 2}}$

Step 2.2.3

Cancel the common factor of $2$ .

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Step 2.2.3.1

Factor $2$ out of $10$ .

$y = 2 \frac{i^{\frac{2}{3}}}{4^{\frac{1}{2 (5)} \cdot 2}}$

Step 2.2.3.2

Cancel the common factor.

$y = 2 \frac{i^{\frac{2}{3}}}{4^{\frac{1}{2 \cdot 5} \cdot 2}}$

Step 2.2.3.3

Rewrite the expression.

$y = 2 \frac{i^{\frac{2}{3}}}{4^{\frac{1}{5}}}$

Step 2.3

Combine $2$ and $\frac{i^{\frac{2}{3}}}{4^{\frac{1}{5}}}$ .

$y = \frac{2 i^{\frac{2}{3}}}{4^{\frac{1}{5}}}$