Solve for n 4(5n-1)^(1/3)-1=0

$4 {(5 n - 1)}^{\frac{1}{3}} - 1 = 0$

Add $1$ to both sides of the equation.

$4 {(5 n - 1)}^{\frac{1}{3}} = 1$

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

${(4 {(5 n - 1)}^{\frac{1}{3}})}^{3} = 1^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${(4 {(5 n - 1)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $4 {(5 n - 1)}^{\frac{1}{3}}$ .

$4^{3} {({(5 n - 1)}^{\frac{1}{3}})}^{3} = 1^{3}$

Raise $4$ to the power of $3$ .

$64 {({(5 n - 1)}^{\frac{1}{3}})}^{3} = 1^{3}$

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

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

$64 {(5 n - 1)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$64 {(5 n - 1)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Rewrite the expression.

$64 {(5 n - 1)}^{1} = 1^{3}$

Simplify.

$64 (5 n - 1) = 1^{3}$

Apply the distributive property.

$64 (5 n) + 64 \cdot - 1 = 1^{3}$

Multiply.

Multiply $5$ by $64$ .

$320 n + 64 \cdot - 1 = 1^{3}$

Multiply $64$ by $- 1$ .

$320 n - 64 = 1^{3}$

Simplify the right side.

One to any power is one.

$320 n - 64 = 1$

Solve for $n$ .

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

Add $64$ to both sides of the equation.

$320 n = 1 + 64$

Add $1$ and $64$ .

$320 n = 65$

Divide each term in $320 n = 65$ by $320$ and simplify.

Divide each term in $320 n = 65$ by $320$ .

$\frac{320 n}{320} = \frac{65}{320}$

Simplify the left side.

Cancel the common factor of $320$ .

Cancel the common factor.

$\frac{320 n}{320} = \frac{65}{320}$

Divide $n$ by $1$ .

$n = \frac{65}{320}$

Simplify the right side.

Cancel the common factor of $65$ and $320$ .

Factor $5$ out of $65$ .

$n = \frac{5 (13)}{320}$

Cancel the common factors.

Factor $5$ out of $320$ .

$n = \frac{5 \cdot 13}{5 \cdot 64}$

Cancel the common factor.

$n = \frac{5 \cdot 13}{5 \cdot 64}$

Rewrite the expression.

$n = \frac{13}{64}$

The result can be shown in multiple forms.

Exact Form:

$n = \frac{13}{64}$

Decimal Form:

$n = 0.203125$

Solve for n 4(5n-1)^(1/3)-1=0

Related Questions

Support LCMGCF.com by disabling your adblocker.