Solve for n 3( fourth root of 2n+6)-6=0

$3 (\sqrt[4]{2 n + 6}) - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$3 \sqrt[4]{2 n + 6} = 6$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${(3 \sqrt[4]{2 n + 6})}^{4} = 6^{4}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 n + 6}$ as ${(2 n + 6)}^{\frac{1}{4}}$ .

${(3 {(2 n + 6)}^{\frac{1}{4}})}^{4} = 6^{4}$

Simplify the left side.

Simplify ${(3 {(2 n + 6)}^{\frac{1}{4}})}^{4}$ .

Apply the product rule to $3 {(2 n + 6)}^{\frac{1}{4}}$ .

$3^{4} {({(2 n + 6)}^{\frac{1}{4}})}^{4} = 6^{4}$

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

$81 {({(2 n + 6)}^{\frac{1}{4}})}^{4} = 6^{4}$

Multiply the exponents in ${({(2 n + 6)}^{\frac{1}{4}})}^{4}$ .

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

$81 {(2 n + 6)}^{\frac{1}{4} \cdot 4} = 6^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$81 {(2 n + 6)}^{\frac{1}{4} \cdot 4} = 6^{4}$

Rewrite the expression.

$81 {(2 n + 6)}^{1} = 6^{4}$

Simplify.

$81 (2 n + 6) = 6^{4}$

Apply the distributive property.

$81 (2 n) + 81 \cdot 6 = 6^{4}$

Multiply.

Multiply $2$ by $81$ .

$162 n + 81 \cdot 6 = 6^{4}$

Multiply $81$ by $6$ .

$162 n + 486 = 6^{4}$

Simplify the right side.

Raise $6$ to the power of $4$ .

$162 n + 486 = 1296$

Step 4

Solve for $n$ .

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

Subtract $486$ from both sides of the equation.

$162 n = 1296 - 486$

Subtract $486$ from $1296$ .

$162 n = 810$

Divide each term in $162 n = 810$ by $162$ and simplify.

Divide each term in $162 n = 810$ by $162$ .

$\frac{162 n}{162} = \frac{810}{162}$

Simplify the left side.

Cancel the common factor of $162$ .

Cancel the common factor.

$\frac{162 n}{162} = \frac{810}{162}$

Divide $n$ by $1$ .

$n = \frac{810}{162}$

Simplify the right side.

Divide $810$ by $162$ .

$n = 5$

Solve for n 3( fourth root of 2n+6)-6=0

Related Questions

Support LCMGCF.com by disabling your adblocker.