Solve for y 3(5y-1)^(1/3)-2=0

$3 {(5 y - 1)}^{\frac{1}{3}} - 2 = 0$

Step 1

Add $2$ to both sides of the equation.

$3 {(5 y - 1)}^{\frac{1}{3}} = 2$

Step 2

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

${(3 {(5 y - 1)}^{\frac{1}{3}})}^{3} = 2^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${(3 {(5 y - 1)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $3 {(5 y - 1)}^{\frac{1}{3}}$ .

$3^{3} {({(5 y - 1)}^{\frac{1}{3}})}^{3} = 2^{3}$

Raise $3$ to the power of $3$ .

$27 {({(5 y - 1)}^{\frac{1}{3}})}^{3} = 2^{3}$

Multiply the exponents in ${({(5 y - 1)}^{\frac{1}{3}})}^{3}$ .

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

$27 {(5 y - 1)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 {(5 y - 1)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

$27 {(5 y - 1)}^{1} = 2^{3}$

Simplify.

$27 (5 y - 1) = 2^{3}$

Apply the distributive property.

$27 (5 y) + 27 \cdot - 1 = 2^{3}$

Multiply.

Multiply $5$ by $27$ .

$135 y + 27 \cdot - 1 = 2^{3}$

Multiply $27$ by $- 1$ .

$135 y - 27 = 2^{3}$

Simplify the right side.

Raise $2$ to the power of $3$ .

$135 y - 27 = 8$

Step 4

Solve for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Add $27$ to both sides of the equation.

$135 y = 8 + 27$

Add $8$ and $27$ .

$135 y = 35$

Divide each term in $135 y = 35$ by $135$ and simplify.

Divide each term in $135 y = 35$ by $135$ .

$\frac{135 y}{135} = \frac{35}{135}$

Simplify the left side.

Cancel the common factor of $135$ .

Cancel the common factor.

$\frac{135 y}{135} = \frac{35}{135}$

Divide $y$ by $1$ .

$y = \frac{35}{135}$

Simplify the right side.

Cancel the common factor of $35$ and $135$ .

Factor $5$ out of $35$ .

$y = \frac{5 (7)}{135}$

Cancel the common factors.

Factor $5$ out of $135$ .

$y = \frac{5 \cdot 7}{5 \cdot 27}$

Cancel the common factor.

$y = \frac{5 \cdot 7}{5 \cdot 27}$

Rewrite the expression.

$y = \frac{7}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{27}$

Decimal Form:

$y = 0.\overline{259}$

Solve for y 3(5y-1)^(1/3)-2=0

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