Solve (1/4)^{2}*(-2/3)^2-{(-2)*(-3)^2-(-4^2)}div(-2)^3

$$( \frac { 1 } { 4 } ) ^ { 2 } \times ( - \frac { 2 } { 3 } ) ^ { 2 } - \{ ( - 2 ) \times ( - 3 ) ^ { 2 } - ( - 4 ^ { 2 } ) \} \div ( - 2 ) ^ { 3 }$$

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

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

$$\frac{1}{16}\left(-\frac{2}{3}\right)^{2}-\frac{-2\left(-3\right)^{2}-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{1}{16}\times \frac{4}{9}-\frac{-2\left(-3\right)^{2}-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

Multiply \frac{1}{16} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{16\times 9}-\frac{-2\left(-3\right)^{2}-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

Do the multiplications in the fraction \frac{1\times 4}{16\times 9}.

$$\frac{4}{144}-\frac{-2\left(-3\right)^{2}-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

Reduce the fraction \frac{4}{144} to lowest terms by extracting and canceling out 4.

$$\frac{1}{36}-\frac{-2\left(-3\right)^{2}-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

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

$$\frac{1}{36}-\frac{-2\times 9-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

Multiply -2 and 9 to get -18.

$$\frac{1}{36}-\frac{-18-\left(-4^{2}\right)}{\left(-2\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{36}-\frac{-18-\left(-16\right)}{\left(-2\right)^{3}}$$

The opposite of -16 is 16.

$$\frac{1}{36}-\frac{-18+16}{\left(-2\right)^{3}}$$

Add -18 and 16 to get -2.

$$\frac{1}{36}-\frac{-2}{\left(-2\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{1}{36}-\frac{-2}{-8}$$

Reduce the fraction \frac{-2}{-8} to lowest terms by extracting and canceling out -2.

$$\frac{1}{36}-\frac{1}{4}$$

Least common multiple of 36 and 4 is 36. Convert \frac{1}{36} and \frac{1}{4} to fractions with denominator 36.

$$\frac{1}{36}-\frac{9}{36}$$

Since \frac{1}{36} and \frac{9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-9}{36}$$

Subtract 9 from 1 to get -8.

$$\frac{-8}{36}$$

Reduce the fraction \frac{-8}{36} to lowest terms by extracting and canceling out 4.

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

Factor

$$-\frac{2}{9} = -0.2222222222222222$$