Solve 0,001^{-1/3}-(-2)^{-2}64^frac{2{3}}-8^-1frac{1{3}}+(9^0)^2

$$0,001 ^ { - \frac { 1 } { 3 } } - ( - 2 ) ^ { - 2 } 64 ^ { \frac { 2 } { 3 } } - 8 ^ { - 1 \frac { 1 } { 3 } } + ( 9 ^ { 0 } ) ^ { 2 }$$

Evaluate

$$-\frac{49}{16}=-3,0625$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 0 and 2 to get 0.

$$0\times 1^{-\frac{1}{3}}-\left(-2\right)^{-2}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

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

$$0\times 1-\left(-2\right)^{-2}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Multiply 0 and 1 to get 0.

$$0-\left(-2\right)^{-2}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$0-\frac{1}{4}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Calculate 64 to the power of \frac{2}{3} and get 16.

$$0-\frac{1}{4}\times 16-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Multiply \frac{1}{4} and 16 to get 4.

$$0-4-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Subtract 4 from 0 to get -4.

$$-4-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Multiply 1 and 3 to get 3.

$$-4-8^{-\frac{3+1}{3}}+9^{0}$$

Add 3 and 1 to get 4.

$$-4-8^{-\frac{4}{3}}+9^{0}$$

Calculate 8 to the power of -\frac{4}{3} and get \frac{1}{16}.

$$-4-\frac{1}{16}+9^{0}$$

Subtract \frac{1}{16} from -4 to get -\frac{65}{16}.

$$-\frac{65}{16}+9^{0}$$

Calculate 9 to the power of 0 and get 1.

$$-\frac{65}{16}+1$$

Add -\frac{65}{16} and 1 to get -\frac{49}{16}.

$$-\frac{49}{16}$$

Factor

$$-\frac{49}{16} = -3\frac{1}{16} = -3.0625$$