Evaluate 3/(2(3)^(1/2))

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

Move ${(3)}^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Multiply $3$ by $3^{- \frac{1}{2}}$ by adding the exponents.

Multiply $3$ by $3^{- \frac{1}{2}}$ .

Raise $3$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$