Finite Math Examples

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

Step 1

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

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

Step 2

Simplify the exponent.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

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

Step 2.1.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.1.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.1.1.1.2.2

Factor $2$ out of $- 2$ .

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

Step 2.1.1.1.2.3

Cancel the common factor.

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

Step 2.1.1.1.2.4

Rewrite the expression.

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

Step 2.1.1.1.3

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.2

Simplify.

$s - 1 = 2^{- 2}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $2^{- 2}$ .

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Step 2.2.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.2.1.2

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

$s - 1 = \frac{1}{4}$

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

$s = \frac{1}{4} + 1$

Step 3.2

Write $1$ as a fraction with a common denominator.

$s = \frac{1}{4} + \frac{4}{4}$

Step 3.3

Combine the numerators over the common denominator.

$s = \frac{1 + 4}{4}$

Step 3.4

Add $1$ and $4$ .

$s = \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \frac{5}{4}$

Decimal Form:

$s = 1.25$

Mixed Number Form:

$s = 1 \frac{1}{4}$