Basic Math Examples

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

Step 1

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

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

Step 2

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

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

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 ${(y^{\frac{1}{5}})}^{5}$ .

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

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

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.

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

Step 3.1.1.1.2.2

Rewrite the expression.

$y^{1} = 2^{5}$

Step 3.1.1.2

Simplify.

$y = 2^{5}$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$y = 32$