Question

prove that 2 raise to power 30 + 2 raise to power 29+ 2 raise to power 28 divided by 2 raise to power 31+ 2 raise to power 30 - 2 raise to power 29=7/10

Answer 1

Hope this helps you to understand

Answer 2

Solution:

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

= $\frac{2^{28}\times2^{2}+2^{28}\times 2^{1}+2^{28}\times1}{2^{28}\times2^{3}+2^{28}\times 2^{2}-2^{28}\times2^{1}}$

/* We know the Exponential Law:

$\boxed {a^{m+n} = a^{m} \times a^{n}}$ */

=$\frac{2^{28}(2^{2}+2+1)}{2^{28}(2^{3}+2^{2}-2}$

/* Take $2^{28}$ common , we get

= $\frac{2^{2}+2+1}{2^{3}+2^{2}-2}$

/* After cancellation, we get

= $\frac{4+2+1}{8+4-2}$

=$\frac{7}{10}$

= RHS

Therefore,

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

=$\frac{7}{10}$

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