Solve for n (5n-6)^(1/3)=1

${(5 n - 6)}^{\frac{1}{3}} = 1$

Step 1

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

${({(5 n - 6)}^{\frac{1}{3}})}^{3} = 1^{3}$

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${({(5 n - 6)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 n - 6)}^{\frac{1}{3}})}^{3}$ .

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

${(5 n - 6)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 n - 6)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Rewrite the expression.

${(5 n - 6)}^{1} = 1^{3}$

Simplify.

$5 n - 6 = 1^{3}$

Simplify the right side.

One to any power is one.

$5 n - 6 = 1$

Step 3

Solve for $n$ .

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

Add $6$ to both sides of the equation.

$5 n = 1 + 6$

Add $1$ and $6$ .

$5 n = 7$

Divide each term in $5 n = 7$ by $5$ and simplify.

Divide each term in $5 n = 7$ by $5$ .

$\frac{5 n}{5} = \frac{7}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{7}{5}$

Divide $n$ by $1$ .

$n = \frac{7}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{7}{5}$

Decimal Form:

$n = 1.4$

Mixed Number Form:

$n = 1 \frac{2}{5}$