Algebra Examples

$16 = {(2 n)}^{\frac{1}{2}} + 10$

Step 1

Rewrite the equation as ${(2 n)}^{\frac{1}{2}} + 10 = 16$ .

${(2 n)}^{\frac{1}{2}} + 10 = 16$

Step 2

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

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Step 2.1

Subtract $10$ from both sides of the equation.

${(2 n)}^{\frac{1}{2}} = 16 - 10$

Step 2.2

Subtract $10$ from $16$ .

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

Step 3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${({(2 n)}^{\frac{1}{2}})}^{2}$ .

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Step 4.1.1.1

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

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.1.2.1

Cancel the common factor.

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

Step 4.1.1.1.2.2

Rewrite the expression.

${(2 n)}^{1} = 6^{2}$

Step 4.1.1.2

Simplify.

$2 n = 6^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Raise $6$ to the power of $2$ .

$2 n = 36$

Step 5

Divide each term in $2 n = 36$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 n = 36$ by $2$ .

$\frac{2 n}{2} = \frac{36}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{36}{2}$

Step 5.2.1.2

Divide $n$ by $1$ .

$n = \frac{36}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $36$ by $2$ .

$n = 18$