Algebra Examples

$v^{\frac{1}{2}} + 1 = 0$

Step 1

Subtract $1$ from both sides of the equation.

$v^{\frac{1}{2}} = - 1$

Step 2

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

${(v^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

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 ${(v^{\frac{1}{2}})}^{2}$ .

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

$v^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Step 3.1.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

$v^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Step 3.1.1.1.2.2

Rewrite the expression.

$v^{1} = {(- 1)}^{2}$

Step 3.1.1.2

Simplify.

$v = {(- 1)}^{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $- 1$ to the power of $2$ .

$v = 1$

Step 4

Exclude the solutions that do not make $v^{\frac{1}{2}} + 1 = 0$ true.

$No solution$