Question

Prove that- ((2^36+(1÷4×2^35)+(1÷8×2^37)) ÷ ((1÷16×2^39)+ (1÷8×2^38)) = 11÷8

Answer 1

Answer:

Step-by-step explan

Answer 2

Concept

Any number a raised to the power x is simplified as multiplying the number a by itself x times.

Given

$[2^{36} + ( 1/4*2^{35} + (1/8*2^{37} ] / [(1/16*2^{39}) + (1/8*2^{38} )] = 11/8$

Find

We have to prove the given equation

Solution

We have,

$[2^{36} + ( 1/4*2^{35} + (1/8*2^{37} ] / [(1/16*2^{39}) + (1/8*2^{38} )] = 11/8$

Simplifying the equation a bit further by writing 4, 8 and 16 as 2 square, cube and 4th power respectively we get

$[2^{36} + ( 1/2^{2} *2^{35} + (1/2^{3} *2^{37} ] / [(1/2^{4} *2^{39}) + (1/2^{3} *2^{38} )] = 11/8$

Cancelling out the terms in denominator we get

$[2^{36} + ( 2^{33} + (2^{34}) ] / [(2^{35}) + (2^{35} )] = 11/8$

Taking out the common terms in the numerator and the denominator we get

$2^{33} (2^{3} + ( 2^{0} + (2^{1}) )/ [2(2^{35} )] = 11/8$

Cancelling out 2^33 from both numerator and denominator

$(2^{3} + ( 2^{0} + (2^{1}) )/ [2(2^{2} )] = 11/8$

Simplifying the equation we get

(8 + 1 + 2)/ (2*4) = 11/8

11/8 = 11/8

Thus, the left hand side is equal to the right hand side

Hence proved.

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