Finite Math Examples

${(3 y - 4)}^{\frac{2}{3}} - 3 {(3 y - 4)}^{- \frac{1}{3}} = 0$

Step 1

Simplify ${(3 y - 4)}^{\frac{2}{3}} - 3 {(3 y - 4)}^{- \frac{1}{3}}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

${(3 y - 4)}^{\frac{2}{3}} - 3 \frac{1}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.1.2

Combine $- 3$ and $\frac{1}{{(3 y - 4)}^{\frac{1}{3}}}$ .

${(3 y - 4)}^{\frac{2}{3}} + \frac{- 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.1.3

Move the negative in front of the fraction.

${(3 y - 4)}^{\frac{2}{3}} - \frac{3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.2

To write ${(3 y - 4)}^{\frac{2}{3}}$ as a fraction with a common denominator, multiply by $\frac{{(3 y - 4)}^{\frac{1}{3}}}{{(3 y - 4)}^{\frac{1}{3}}}$ .

$\frac{{(3 y - 4)}^{\frac{2}{3}} {(3 y - 4)}^{\frac{1}{3}}}{{(3 y - 4)}^{\frac{1}{3}}} - \frac{3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.3

Combine the numerators over the common denominator.

$\frac{{(3 y - 4)}^{\frac{2}{3}} {(3 y - 4)}^{\frac{1}{3}} - 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply ${(3 y - 4)}^{\frac{2}{3}}$ by ${(3 y - 4)}^{\frac{1}{3}}$ by adding the exponents.

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Step 1.4.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(3 y - 4)}^{\frac{2}{3} + \frac{1}{3}} - 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.4.1.2

Combine the numerators over the common denominator.

$\frac{{(3 y - 4)}^{\frac{2 + 1}{3}} - 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.4.1.3

Add $2$ and $1$ .

$\frac{{(3 y - 4)}^{\frac{3}{3}} - 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.4.1.4

Divide $3$ by $3$ .

$\frac{{(3 y - 4)}^{1} - 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.4.2

Simplify ${(3 y - 4)}^{1}$ .

$\frac{3 y - 4 - 3}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 1.4.3

Subtract $3$ from $- 4$ .

$\frac{3 y - 7}{{(3 y - 4)}^{\frac{1}{3}}} = 0$

Step 2

Set the numerator equal to zero.

$3 y - 7 = 0$

Step 3

Solve the equation for $y$ .

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Step 3.1

Add $7$ to both sides of the equation.

$3 y = 7$

Step 3.2

Divide each term in $3 y = 7$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 y = 7$ by $3$ .

$\frac{3 y}{3} = \frac{7}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{7}{3}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{3}$

Decimal Form:

$y = 2.\overline{3}$

Mixed Number Form:

$y = 2 \frac{1}{3}$