Question

Find the value of: $\frac{2^{30}+2^{29}+2^{28}}{2^{31}+2^{30}-2^{29}}$

Answer 1

Consider the L.H.S,

$=\frac{2^{30}+2^{29}+2^{28}}{2^{31}+2^{30}-2^{29}}$

$=\frac{2^{28}}{2^{29}}\times \left(\frac{4+2+1}{4+2-1}\right)$

$=\frac{1}{2}\times \left(\frac{7}{5}\right)$

$=\frac{7}{10}$

Hence, this is the required value.