Evaluate 3^(1/2-1)

$3^{\frac{1}{2} - 1}$

Step 1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3^{\frac{1}{2} - 1 \cdot \frac{2}{2}}$

Step 2

Combine $- 1$ and $\frac{2}{2}$ .

$3^{\frac{1}{2} + \frac{- 1 \cdot 2}{2}}$

Step 3

Combine the numerators over the common denominator.

$3^{\frac{1 - 1 \cdot 2}{2}}$

Step 4

Simplify the numerator.

Multiply $- 1$ by $2$ .

$3^{\frac{1 - 2}{2}}$

Subtract $2$ from $1$ .

$3^{\frac{- 1}{2}}$

Step 5

Move the negative in front of the fraction.

$3^{- \frac{1}{2}}$

Step 6

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

$\frac{1}{3^{\frac{1}{2}}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3^{\frac{1}{2}}}$

Decimal Form:

$0.57735026 \dots$