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Plzzz ans.. this...!!! prove that 2^36+(1/4×2^35) + (1/8×2^37) ÷ (1/16×2^39) + 1/8×2^38) = 11/8​

Answer»

Let's take LHS and PROVE it to be equal to RHS

= \frac{ {2}^{36} + ( \frac{1}{4} \times {2}^{35} ) + ( \frac{1}{8} \times {2}^{37} )}{ (\frac{1}{16} \times {2}^{39} ) + (\frac{1}{8} \times {2}^{38} )} \\ \\ = \frac{ {2}^{36} + ( \frac{1}{ {2}^{2} } \times {2}^{35} ) + ( \frac{1}{ {2}^{3} } \times {2}^{37} )}{ (\frac{1}{ {2}^{4} } \times {2}^{39} ) + (\frac{1}{ {2}^{3} } \times {2}^{38} )} \\ \\ = \frac{ {2}^{36} + ( {2}^{35 - 2} ) + ( {2}^{37 - 3} )}{ ( {2}^{39 - 4} ) + ( {2}^{38 - 3} )} \\ \\ = \frac{ {2}^{36} + ( {2}^{33} ) + ( {2}^{34} )}{ ( {2}^{35} ) + ( {2}^{35} )} \\ \\ = \frac{ {2}^{33} ( {2}^{3} + 1 + {2}) }{ {2}^{33}( {2}^{2} + {2}^{2}) }

Here 2^33 cancels because it is common on both NUMERATOR and DENOMINATOR

= \frac{2 ^{3} + 3}{4 + 4} \\ \\ = \frac{8 + 3}{8} \\ \\ = \frac{11}{8}

HENCE PROVED!



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