Solve 2^-5*0.5^-4+3^-2*(1/3)^-3

$$2 ^ { - 5 } \times 0.5 ^ { - 4 } + 3 ^ { - 2 } \times ( \frac { 1 } { 3 } ) ^ { - 3 }$$

Evaluate

$$3.5$$

Solution Steps

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{1}{32}\times 0.5^{-4}+3^{-2}\times \left(\frac{1}{3}\right)^{-3}$$

Calculate 0.5 to the power of -4 and get 16.

$$\frac{1}{32}\times 16+3^{-2}\times \left(\frac{1}{3}\right)^{-3}$$

Multiply \frac{1}{32} and 16 to get \frac{1}{2}.

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

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

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

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

$$\frac{1}{2}+\frac{1}{9}\times 27$$

Multiply \frac{1}{9} and 27 to get 3.

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

Add \frac{1}{2} and 3 to get \frac{7}{2}.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$