Solve (3^-1,5+81^-frac{1{2}})(3^-frac{3{2}}-3^-2)

$$( 3 ^ { - 1,5 } + 81 ^ { - \frac { 1 } { 2 } } ) ( 3 ^ { - \frac { 3 } { 2 } } - 3 ^ { - 2 } )$$

Evaluate

$$\frac{2}{81}\approx 0,024691358$$

Solution Steps

Calculate 81 to the power of -\frac{1}{2} and get \frac{1}{9}.

$$\left(3^{-1,5}+\frac{1}{9}\right)\left(3^{-\frac{3}{2}}-3^{-2}\right)$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\left(3^{-1,5}+\frac{1}{9}\right)\left(3^{-\frac{3}{2}}-\frac{1}{9}\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square \frac{1}{9}.

$$\left(3^{-\frac{3}{2}}\right)^{2}-\frac{1}{81}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{3}{2} and 2 to get -3.

$$3^{-3}-\frac{1}{81}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{1}{27}-\frac{1}{81}$$

Subtract \frac{1}{81} from \frac{1}{27} to get \frac{2}{81}.

$$\frac{2}{81}$$

Factor

$$\frac{2}{3 ^ {4}} = 0.024691358024691357$$