Solve 3^-frac{5{2}}:3^-frac{2{3}}

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

Evaluate

$$\frac{\sqrt[6]{3}}{9}\approx 0.133437439$$

Steps for Raising Power to Another Power

Rewrite 3^{-\frac{2}{3}} as 3^{-\frac{5}{2}}\times 3^{\frac{11}{6}}. Cancel out 3^{-\frac{5}{2}} in both numerator and denominator.

$$\frac{1}{3^{\frac{11}{6}}}$$

To raise a power to another power, multiply the exponents.

$$3^{\frac{11}{6}\left(-1\right)}$$

Multiply \frac{11}{6} times -1.

$$3^{-\frac{11}{6}}$$

Raise 3 to the power -\frac{11}{6}.

$$\frac{1}{3\times 3^{\frac{5}{6}}}$$