Solve [7/2]^3div[5/4]^2+(1-1)^5/8

$$[ \frac { 7 } { 2 } ] ^ { 3 } \div [ \frac { 5 } { 4 } ] ^ { 2 } + \frac { ( 1 - 1 ) ^ { 5 } } { 8 }$$

Evaluate

$$\frac{686}{25}=27.44$$

Solution Steps

Calculate \frac{7}{2} to the power of 3 and get \frac{343}{8}.

$$\frac{\frac{343}{8}}{\left(\frac{5}{4}\right)^{2}}+\frac{\left(1-1\right)^{5}}{8}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{\frac{343}{8}}{\frac{25}{16}}+\frac{\left(1-1\right)^{5}}{8}$$

Divide \frac{343}{8} by \frac{25}{16} by multiplying \frac{343}{8} by the reciprocal of \frac{25}{16}.

$$\frac{343}{8}\times \frac{16}{25}+\frac{\left(1-1\right)^{5}}{8}$$

Multiply \frac{343}{8} and \frac{16}{25} to get \frac{686}{25}.

$$\frac{686}{25}+\frac{\left(1-1\right)^{5}}{8}$$

Subtract 1 from 1 to get 0.

$$\frac{686}{25}+\frac{0^{5}}{8}$$

Calculate 0 to the power of 5 and get 0.

$$\frac{686}{25}+\frac{0}{8}$$

Zero divided by any non-zero number gives zero.

$$\frac{686}{25}+0$$

Add \frac{686}{25} and 0 to get \frac{686}{25}.

$$\frac{686}{25}$$

Factor

$$\frac{2 \cdot 7 ^ {3}}{5 ^ {2}} = 27\frac{11}{25} = 27.44$$