Solve frac{(-1)^{8}-(-3)*2^2+1^2}{36:(-3)^2-2^2*2}

$$\frac { ( - 1 ) ^ { 8 } - ( - 3 ) \cdot 2 ^ { 2 } + 1 ^ { 2 } } { 36 : ( - 3 ) ^ { 2 } - 2 ^ { 2 } \cdot 2 }$$

Evaluate

$$-\frac{7}{2}=-3.5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\left(-1\right)^{8}-\left(-3\times 2^{2}\right)+1^{2}}{\frac{36}{\left(-3\right)^{2}}-2^{3}}$$

Calculate -1 to the power of 8 and get 1.

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

Calculate 2 to the power of 2 and get 4.

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

Multiply -3 and 4 to get -12.

$$\frac{1-\left(-12\right)+1^{2}}{\frac{36}{\left(-3\right)^{2}}-2^{3}}$$

The opposite of -12 is 12.

$$\frac{1+12+1^{2}}{\frac{36}{\left(-3\right)^{2}}-2^{3}}$$

Add 1 and 12 to get 13.

$$\frac{13+1^{2}}{\frac{36}{\left(-3\right)^{2}}-2^{3}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{13+1}{\frac{36}{\left(-3\right)^{2}}-2^{3}}$$

Add 13 and 1 to get 14.

$$\frac{14}{\frac{36}{\left(-3\right)^{2}}-2^{3}}$$

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

$$\frac{14}{\frac{36}{9}-2^{3}}$$

Divide 36 by 9 to get 4.

$$\frac{14}{4-2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{14}{4-8}$$

Subtract 8 from 4 to get -4.

$$\frac{14}{-4}$$

Reduce the fraction \frac{14}{-4} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{2}$$

Factor

$$-\frac{7}{2} = -3\frac{1}{2} = -3.5$$