Solve 2^{-1}+(5^{2})^3*5^-6+4^-3*32-2*(-3)^2*1/9

$$2 ^ { - 1 } + ( 5 ^ { 2 } ) ^ { 3 } \cdot 5 ^ { - 6 } + 4 ^ { - 3 } \cdot 32 - 2 \cdot ( - 3 ) ^ { 2 } \cdot \frac { 1 } { 9 }$$

Evaluate

$$0$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2^{-1}+5^{6}\times 5^{-6}+4^{-3}\times 32-2\left(-3\right)^{2}\times \frac{1}{9}$$

Multiply 5^{6} and 5^{-6} to get 1.

$$2^{-1}+1+4^{-3}\times 32-2\left(-3\right)^{2}\times \frac{1}{9}$$

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

$$\frac{1}{2}+1+4^{-3}\times 32-2\left(-3\right)^{2}\times \frac{1}{9}$$

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

$$\frac{3}{2}+4^{-3}\times 32-2\left(-3\right)^{2}\times \frac{1}{9}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{3}{2}+\frac{1}{64}\times 32-2\left(-3\right)^{2}\times \frac{1}{9}$$

Multiply \frac{1}{64} and 32 to get \frac{1}{2}.

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

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

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

Calculate -3 to the power of 2 and get 9.

$$2-2\times 9\times \frac{1}{9}$$

Multiply 2 and 9 to get 18.

$$2-18\times \frac{1}{9}$$

Multiply 18 and \frac{1}{9} to get 2.

$$2-2$$

Subtract 2 from 2 to get 0.

$$0$$

Factor

$$0$$