Solve 5^{2}*(-1/5)^2+2^3*(-1/2)^4-(-1)^15

$$5 ^ { 2 } \times ( - \frac { 1 } { 5 } ) ^ { 2 } + 2 ^ { 3 } \times ( - \frac { 1 } { 2 } ) ^ { 4 } - ( - 1 ) ^ { 15 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25\left(-\frac{1}{5}\right)^{2}+2^{3}\left(-\frac{1}{2}\right)^{4}-\left(-1\right)^{15}$$

Calculate -\frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$25\times \frac{1}{25}+2^{3}\left(-\frac{1}{2}\right)^{4}-\left(-1\right)^{15}$$

Cancel out 25 and 25.

$$1+2^{3}\left(-\frac{1}{2}\right)^{4}-\left(-1\right)^{15}$$

Calculate 2 to the power of 3 and get 8.

$$1+8\left(-\frac{1}{2}\right)^{4}-\left(-1\right)^{15}$$

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

$$1+8\times \frac{1}{16}-\left(-1\right)^{15}$$

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

$$1+\frac{8}{16}-\left(-1\right)^{15}$$

Reduce the fraction \frac{8}{16} to lowest terms by extracting and canceling out 8.

$$1+\frac{1}{2}-\left(-1\right)^{15}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}+\frac{1}{2}-\left(-1\right)^{15}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{2}-\left(-1\right)^{15}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}-\left(-1\right)^{15}$$

Calculate -1 to the power of 15 and get -1.

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

The opposite of -1 is 1.

$$\frac{3}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{3}{2}+\frac{2}{2}$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{2}$$

Add 3 and 2 to get 5.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$