Solve (23/5)^0+2^-2*(21/4)^-frac{1{2}}-(0.01)^0.5

$$( 2 \frac { 3 } { 5 } ) ^ { 0 } + 2 ^ { - 2 } \times ( 2 \frac { 1 } { 4 } ) ^ { - \frac { 1 } { 2 } } - ( 0.01 ) ^ { 0.5 }$$

Evaluate

$$\frac{16}{15}\approx 1.066666667$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\left(\frac{10+3}{5}\right)^{0}+2^{-2}\times \left(\frac{2\times 4+1}{4}\right)^{-\frac{1}{2}}-0.01^{0.5}$$

Add 10 and 3 to get 13.

$$\left(\frac{13}{5}\right)^{0}+2^{-2}\times \left(\frac{2\times 4+1}{4}\right)^{-\frac{1}{2}}-0.01^{0.5}$$

Calculate \frac{13}{5} to the power of 0 and get 1.

$$1+2^{-2}\times \left(\frac{2\times 4+1}{4}\right)^{-\frac{1}{2}}-0.01^{0.5}$$

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

$$1+\frac{1}{4}\times \left(\frac{2\times 4+1}{4}\right)^{-\frac{1}{2}}-0.01^{0.5}$$

Multiply 2 and 4 to get 8.

$$1+\frac{1}{4}\times \left(\frac{8+1}{4}\right)^{-\frac{1}{2}}-0.01^{0.5}$$

Add 8 and 1 to get 9.

$$1+\frac{1}{4}\times \left(\frac{9}{4}\right)^{-\frac{1}{2}}-0.01^{0.5}$$

Calculate \frac{9}{4} to the power of -\frac{1}{2} and get \frac{2}{3}.

$$1+\frac{1}{4}\times \frac{2}{3}-0.01^{0.5}$$

Multiply \frac{1}{4} and \frac{2}{3} to get \frac{1}{6}.

$$1+\frac{1}{6}-0.01^{0.5}$$

Add 1 and \frac{1}{6} to get \frac{7}{6}.

$$\frac{7}{6}-0.01^{0.5}$$

Calculate 0.01 to the power of 0.5 and get \frac{1}{10}.

$$\frac{7}{6}-\frac{1}{10}$$

Subtract \frac{1}{10} from \frac{7}{6} to get \frac{16}{15}.

$$\frac{16}{15}$$

Factor

$$\frac{2 ^ {4}}{3 \cdot 5} = 1\frac{1}{15} = 1.0666666666666667$$