Basic Math Examples

$\frac{2}{5} = a^{\frac{1}{5}}$

Step 1

Rewrite the equation as $a^{\frac{1}{5}} = \frac{2}{5}$ .

$a^{\frac{1}{5}} = \frac{2}{5}$

Step 2

Raise each side of the equation to the power of $5$ to eliminate the fractional exponent on the left side.

${(a^{\frac{1}{5}})}^{5} = {(\frac{2}{5})}^{5}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(a^{\frac{1}{5}})}^{5}$ .

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Step 3.1.1.1

Multiply the exponents in ${(a^{\frac{1}{5}})}^{5}$ .

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Step 3.1.1.1.1

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

$a^{\frac{1}{5} \cdot 5} = {(\frac{2}{5})}^{5}$

Step 3.1.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

$a^{\frac{1}{5} \cdot 5} = {(\frac{2}{5})}^{5}$

Step 3.1.1.1.2.2

Rewrite the expression.

$a^{1} = {(\frac{2}{5})}^{5}$

Step 3.1.1.2

Simplify.

$a = {(\frac{2}{5})}^{5}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify ${(\frac{2}{5})}^{5}$ .

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Step 3.2.1.1

Apply the product rule to $\frac{2}{5}$ .

$a = \frac{2^{5}}{5^{5}}$

Step 3.2.1.2

Raise $2$ to the power of $5$ .

$a = \frac{32}{5^{5}}$

Step 3.2.1.3

Raise $5$ to the power of $5$ .

$a = \frac{32}{3125}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{32}{3125}$

Decimal Form:

$a = 0.01024$