Calculus Examples

$x^{- \frac{1}{3}} = 1$

Step 1

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

${(x^{- \frac{1}{3}})}^{- 3} = 1^{- 3}$

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 ${(x^{- \frac{1}{3}})}^{- 3}$ .

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

$x^{- \frac{1}{3} \cdot - 3} = 1^{- 3}$

Step 2.1.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.1.2.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$x^{\frac{- 1}{3} \cdot - 3} = 1^{- 3}$

Step 2.1.1.1.2.2

Factor $3$ out of $- 3$ .

$x^{\frac{- 1}{3} \cdot (3 (- 1))} = 1^{- 3}$

Step 2.1.1.1.2.3

Cancel the common factor.

$x^{\frac{- 1}{3} \cdot (3 \cdot - 1)} = 1^{- 3}$

Step 2.1.1.1.2.4

Rewrite the expression.

$x^{- 1 \cdot - 1} = 1^{- 3}$

Step 2.1.1.1.3

Multiply $- 1$ by $- 1$ .

$x^{1} = 1^{- 3}$

Step 2.1.1.2

Simplify.

$x = 1^{- 3}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $1^{- 3}$ .

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Step 2.2.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = \frac{1}{1^{3}}$

Step 2.2.1.2

One to any power is one.

$x = \frac{1}{1}$

Step 2.2.1.3

Divide $1$ by $1$ .

$x = 1$