Algebra Examples

${(2 m + 1)}^{\frac{1}{4}} - 2 = 1$

Step 1

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

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Step 1.1

Add $2$ to both sides of the equation.

${(2 m + 1)}^{\frac{1}{4}} = 1 + 2$

Step 1.2

Add $1$ and $2$ .

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

Step 2

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

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

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${({(2 m + 1)}^{\frac{1}{4}})}^{4}$ .

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

${(2 m + 1)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Step 3.1.1.1.2

Cancel the common factor of $4$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

${(2 m + 1)}^{\frac{1}{4} \cdot 4} = 3^{4}$

Step 3.1.1.1.2.2

Rewrite the expression.

${(2 m + 1)}^{1} = 3^{4}$

Step 3.1.1.2

Simplify.

$2 m + 1 = 3^{4}$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$2 m + 1 = 81$

Step 4

Solve for $m$ .

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Step 4.1

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

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Step 4.1.1

Subtract $1$ from both sides of the equation.

$2 m = 81 - 1$

Step 4.1.2

Subtract $1$ from $81$ .

$2 m = 80$

Step 4.2

Divide each term in $2 m = 80$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 m = 80$ by $2$ .

$\frac{2 m}{2} = \frac{80}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 m}{2} = \frac{80}{2}$

Step 4.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{80}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $80$ by $2$ .

$m = 40$