Solve (-2)^{2}:4^{2}-4^{2}:(-2)^{3}-[(-1)^3-(-1)^3*(-1)^2]+(1)^7

$$( - 2 ) ^ { 2 } : 4 ^ { 2 } - 4 ^ { 2 } : ( - 2 ) ^ { 3 } - [ ( - 1 ) ^ { 3 } - ( - 1 ) ^ { 3 } \cdot ( - 1 ) ^ { 2 } ] + ( 1 ) ^ { 7 }$$

Evaluate

$$\frac{13}{4}=3.25$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\left(-2\right)^{2}}{4^{2}}-\frac{4^{2}}{\left(-2\right)^{3}}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4}{4^{2}}-\frac{4^{2}}{\left(-2\right)^{3}}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{4}{16}-\frac{4^{2}}{\left(-2\right)^{3}}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}-\frac{4^{2}}{\left(-2\right)^{3}}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{4}-\frac{16}{\left(-2\right)^{3}}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

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

$$\frac{1}{4}-\frac{16}{-8}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Divide 16 by -8 to get -2.

$$\frac{1}{4}-\left(-2\right)-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

The opposite of -2 is 2.

$$\frac{1}{4}+2-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{1}{4}+\frac{8}{4}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+8}{4}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Add 1 and 8 to get 9.

$$\frac{9}{4}-\left(\left(-1\right)^{3}-\left(-1\right)^{5}\right)+1^{7}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{9}{4}-\left(-1-\left(-1\right)^{5}\right)+1^{7}$$

Calculate -1 to the power of 5 and get -1.

$$\frac{9}{4}-\left(-1-\left(-1\right)\right)+1^{7}$$

The opposite of -1 is 1.

$$\frac{9}{4}-\left(-1+1\right)+1^{7}$$

Add -1 and 1 to get 0.

$$\frac{9}{4}-0+1^{7}$$

Subtract 0 from \frac{9}{4} to get \frac{9}{4}.

$$\frac{9}{4}+1^{7}$$

Calculate 1 to the power of 7 and get 1.

$$\frac{9}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{9}{4}+\frac{4}{4}$$

Since \frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{4}$$

Add 9 and 4 to get 13.

$$\frac{13}{4}$$

Factor

$$\frac{13}{2 ^ {2}} = 3\frac{1}{4} = 3.25$$