Solve {left(28/15-14/4/frac{33{27}}right)}^2

$${ \left( \frac{ 28 }{ 15 } - \frac{ \frac{ 14 }{ 4 } }{ \frac{ 33 }{ 27 } } \right) }^{ 2 }$$

Evaluate

$$\frac{108241}{108900}\approx 0.993948577$$

Solution Steps

Divide \frac{14}{4} by \frac{33}{27} by multiplying \frac{14}{4} by the reciprocal of \frac{33}{27}.

$$\left(\frac{28}{15}-\frac{14\times 27}{4\times 33}\right)^{2}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\left(\frac{28}{15}-\frac{7\times 9}{2\times 11}\right)^{2}$$

Multiply 7 and 9 to get 63.

$$\left(\frac{28}{15}-\frac{63}{2\times 11}\right)^{2}$$

Multiply 2 and 11 to get 22.

$$\left(\frac{28}{15}-\frac{63}{22}\right)^{2}$$

Subtract \frac{63}{22} from \frac{28}{15} to get -\frac{329}{330}.

$$\left(-\frac{329}{330}\right)^{2}$$

Calculate -\frac{329}{330} to the power of 2 and get \frac{108241}{108900}.

$$\frac{108241}{108900}$$

Factor

$$\frac{7 ^ {2} \cdot 47 ^ {2}}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2} \cdot 11 ^ {2}} = 0.9939485766758493$$