Calculus Examples

\frac{2}{3} x^{- \frac{1}{3}} = 0

$\frac{2}{3} x^{- \frac{1}{3}} = 0$

Step 1

Multiply both sides of the equation by

\frac{3}{2}

$\frac{3}{2}$ .

\frac{3}{2} (\frac{2}{3} x^{- \frac{1}{3}}) = \frac{3}{2} \cdot 0

$\frac{3}{2} (\frac{2}{3} x^{- \frac{1}{3}}) = \frac{3}{2} \cdot 0$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

\frac{3}{2} (\frac{2}{3} x^{- \frac{1}{3}})

$\frac{3}{2} (\frac{2}{3} x^{- \frac{1}{3}})$ .

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Step 2.1.1.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{3}{2} (\frac{2}{3} \cdot \frac{1}{x^{\frac{1}{3}}}) = \frac{3}{2} \cdot 0

$\frac{3}{2} (\frac{2}{3} \cdot \frac{1}{x^{\frac{1}{3}}}) = \frac{3}{2} \cdot 0$

Step 2.1.1.2

Combine.

\frac{3}{2} \cdot \frac{2 \cdot 1}{3 x^{\frac{1}{3}}} = \frac{3}{2} \cdot 0

$\frac{3}{2} \cdot \frac{2 \cdot 1}{3 x^{\frac{1}{3}}} = \frac{3}{2} \cdot 0$

Step 2.1.1.3

Combine.

\frac{3 (2 \cdot 1)}{2 (3 x^{\frac{1}{3}})} = \frac{3}{2} \cdot 0

$\frac{3 (2 \cdot 1)}{2 (3 x^{\frac{1}{3}})} = \frac{3}{2} \cdot 0$

Step 2.1.1.4

Cancel the common factor.

$\frac{3 (2 \cdot 1)}{2 (3 x^{\frac{1}{3}})} = \frac{3}{2} \cdot 0$

Step 2.1.1.5

Rewrite the expression.

$\frac{2 \cdot 1}{2 (x^{\frac{1}{3}})} = \frac{3}{2} \cdot 0$

Step 2.1.1.6

Cancel the common factor.

$\frac{2 \cdot 1}{2 x^{\frac{1}{3}}} = \frac{3}{2} \cdot 0$

Step 2.1.1.7

Rewrite the expression.

$\frac{1}{x^{\frac{1}{3}}} = \frac{3}{2} \cdot 0$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply

$\frac{3}{2}$ by

$0$ .

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

Step 3

Set the numerator equal to zero.

$1 = 0$

Step 4

Since

$1 \neq 0$ , there are no solutions.

No solution