Evaluate (1/5)^(1/2+1)

${(\frac{1}{5})}^{\frac{1}{2} + 1}$

Step 1

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

${(\frac{1}{5})}^{\frac{1}{2} + \frac{2}{2}}$

Step 2

Combine the numerators over the common denominator.

${(\frac{1}{5})}^{\frac{1 + 2}{2}}$

Step 3

Add $1$ and $2$ .

${(\frac{1}{5})}^{\frac{3}{2}}$

Step 4

Apply the product rule to $\frac{1}{5}$ .

$\frac{1^{\frac{3}{2}}}{5^{\frac{3}{2}}}$

Step 5

One to any power is one.

$\frac{1}{5^{\frac{3}{2}}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5^{\frac{3}{2}}}$

Decimal Form:

$0.08944271 \dots$