Solve [1^{-10}+pi^{0}-(0.2^{3}-8/1000)^{2}]*4^-2-27^frac{1{3}}+2^-2divsqrt{(-1/7)^2}

$$[ 1 ^ { - 10 } + \pi ^ { 0 } - ( 0.2 ^ { 3 } - \frac { 8 } { 1000 } ) ^ { 2 } ] \times 4 ^ { - 2 } - 27 ^ { \frac { 1 } { 3 } } + 2 ^ { - 2 } \div \sqrt { ( - \frac { 1 } { 7 } ) ^ { 2 } }$$

Evaluate

$$-1.125$$

Solution Steps

Calculate 1 to the power of -10 and get 1.

$$\left(1+\pi ^{0}-\left(0.2^{3}-\frac{8}{1000}\right)^{2}\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Calculate \pi to the power of 0 and get 1.

$$\left(1+1-\left(0.2^{3}-\frac{8}{1000}\right)^{2}\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Add 1 and 1 to get 2.

$$\left(2-\left(0.2^{3}-\frac{8}{1000}\right)^{2}\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Calculate 0.2 to the power of 3 and get 0.008.

$$\left(2-\left(0.008-\frac{8}{1000}\right)^{2}\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Reduce the fraction \frac{8}{1000} to lowest terms by extracting and canceling out 8.

$$\left(2-\left(0.008-\frac{1}{125}\right)^{2}\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Subtract \frac{1}{125} from 0.008 to get 0.

$$\left(2-0^{2}\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Calculate 0 to the power of 2 and get 0.

$$\left(2-0\right)\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Subtract 0 from 2 to get 2.

$$2\times 4^{-2}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$2\times \frac{1}{16}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Multiply 2 and \frac{1}{16} to get \frac{1}{8}.

$$\frac{1}{8}-27^{\frac{1}{3}}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

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

$$\frac{1}{8}-3+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Subtract 3 from \frac{1}{8} to get -\frac{23}{8}.

$$-\frac{23}{8}+\frac{2^{-2}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

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

$$-\frac{23}{8}+\frac{\frac{1}{4}}{\sqrt{\left(-\frac{1}{7}\right)^{2}}}$$

Calculate -\frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$-\frac{23}{8}+\frac{\frac{1}{4}}{\sqrt{\frac{1}{49}}}$$

Rewrite the square root of the division \frac{1}{49} as the division of square roots \frac{\sqrt{1}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$-\frac{23}{8}+\frac{\frac{1}{4}}{\frac{1}{7}}$$

Divide \frac{1}{4} by \frac{1}{7} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{7}.

$$-\frac{23}{8}+\frac{1}{4}\times 7$$

Multiply \frac{1}{4} and 7 to get \frac{7}{4}.

$$-\frac{23}{8}+\frac{7}{4}$$

Add -\frac{23}{8} and \frac{7}{4} to get -\frac{9}{8}.

$$-\frac{9}{8}$$

Factor

$$-1.125$$