Calculus Examples

$y^{\frac{1}{3}} = 0$

Step 1

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(y^{\frac{1}{3}})}^{3} = 0^{3}$

Step 2

Simplify the exponent.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify ${(y^{\frac{1}{3}})}^{3}$ .

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Step 2.1.1.1

Multiply the exponents in ${(y^{\frac{1}{3}})}^{3}$ .

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Step 2.1.1.1.1

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

$y^{\frac{1}{3} \cdot 3} = 0^{3}$

Step 2.1.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.1.2.1

Cancel the common factor.

$y^{\frac{1}{3} \cdot 3} = 0^{3}$

Step 2.1.1.1.2.2

Rewrite the expression.

$y^{1} = 0^{3}$

Step 2.1.1.2

Simplify.

$y = 0^{3}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Raising $0$ to any positive power yields $0$ .

$y = 0$