Question

(1÷4)×(2÷6)×(3÷8)×(4÷10)×(5÷12)×-----×(31÷64)=(1÷2^x) the value of x is????

Answer 1

The value of x will be equal to 36.

Step-by-step explanation:

We have,

(1÷4)×(2÷6)×(3÷8)×(4÷10)×(5÷12)×..........×(31÷64)

= $\dfrac{1 \times 2 \times 3\times .............. \times 31}{4 \times 6 \times 8 \times ............. \times 64 }$

= $\dfrac{[1 \times 2 \times 3 \times .................... \times 31] \times 2}{2 \times 4 \times 6 \times ................ \times 64}$ {Multiplying 2 with both numerator and denominator}

= $\dfrac{[1 \times 2 \times 3 \times .................... \times 31] \times 2}{(2 \times 1) \times (2 \times 2) \times (2\times 3) \times ................ \times (2 \times 32)}$  

= $\dfrac{[1 \times 2 \times 3 \times .................... \times 31] \times 2}{(2^{32})[ 1 \times 2 \times 3 \times ................ \times 32]}$ {Taking 2 common from each 32 terms}

= $\dfrac{2}{2^{32} \times 32}$ {Canceling 31! from numerator and denominator}

= $\dfrac{1}{2^{32}\times 16}$

= $\dfrac{1}{2^{32} \times 2^{4}}$ {Since $16 = 2^{4}$ }

= $\dfrac{1}{2^{36}}$

Therefore, the value of x will be equal to 36. (Answer)