Calculus Examples

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

Step 1

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

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

Step 2

Simplify the exponent.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

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

Tap for more steps...

Step 2.1.1.1.1

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

$x^{- \frac{1}{2} \cdot - 2} = 2^{- 2}$

Step 2.1.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.1.2.1

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

$x^{\frac{- 1}{2} \cdot - 2} = 2^{- 2}$

Step 2.1.1.1.2.2

Factor $2$ out of $- 2$ .

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

Step 2.1.1.1.2.3

Cancel the common factor.

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

Step 2.1.1.1.2.4

Rewrite the expression.

$x^{- 1 \cdot - 1} = 2^{- 2}$

Step 2.1.1.1.3

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.2

Simplify.

$x = 2^{- 2}$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $2^{- 2}$ .

Tap for more steps...

Step 2.2.1.1

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

$x = \frac{1}{2^{2}}$

Step 2.2.1.2

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.25$