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

$$6.9375$$

Solution Steps

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

$$0.001^{-\frac{1}{3}}-\left(-2\right)^{-2}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Calculate 0.001 to the power of -\frac{1}{3} and get 10.

$$10-\left(-2\right)^{-2}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

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

$$10-\frac{1}{4}\times 64^{\frac{2}{3}}-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

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

$$10-\frac{1}{4}\times 16-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

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

$$10-4-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Subtract 4 from 10 to get 6.

$$6-8^{-\frac{1\times 3+1}{3}}+9^{0}$$

Multiply 1 and 3 to get 3.

$$6-8^{-\frac{3+1}{3}}+9^{0}$$

Add 3 and 1 to get 4.

$$6-8^{-\frac{4}{3}}+9^{0}$$

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

$$6-\frac{1}{16}+9^{0}$$

Subtract \frac{1}{16} from 6 to get \frac{95}{16}.

$$\frac{95}{16}+9^{0}$$

Calculate 9 to the power of 0 and get 1.

$$\frac{95}{16}+1$$

Add \frac{95}{16} and 1 to get \frac{111}{16}.

$$\frac{111}{16}$$

Factor

$$\frac{3 \cdot 37}{2 ^ {4}} = 6\frac{15}{16} = 6.9375$$