Convert to Radical Form 2^-1.5

$2^{- 1.5}$

Change $- 1.5$ into a fraction.

Multiply by $\frac{10}{10}$ to remove the decimal.

$2^{\frac{10 \cdot - 1.5}{10}}$

Multiply $10$ by $- 1.5$ .

$2^{\frac{- 15}{10}}$

Move the negative in front of the fraction.

$2^{- \frac{15}{10}}$

Cancel the common factor of $15$ and $10$ .

Factor $5$ out of $15$ .

$2^{- \frac{5 (3)}{10}}$

Cancel the common factors.

Factor $5$ out of $10$ .

$2^{- \frac{5 \cdot 3}{5 \cdot 2}}$

Cancel the common factor.

$2^{- \frac{5 \cdot 3}{5 \cdot 2}}$

Rewrite the expression.

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

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

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

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.35355339 \dots$