Question

Find the exponent of 2 in x = 20 x 19 x 18x...
11.​

Answer 1

Answer:

x1/2

exponent of 2in x

x1/2

Answer 2

The exponent of 2 in x is 10.

Step-by-step explanation:

x = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11

20 can be written as $2^{2} \times 5$.

18 can be written as 2 x 9.

16 can be written as $2^{4}$.

14 can be written as 2 x 7.

12 can be written as $2^{2} \times 3$.

So, x = $2^{2} \times 5\times 19\times 2\times 9\times 17\times 2^{4}\times 15\times 2\times 7\times 13\times 2^{2}\times 3\times 11$

x = $2^{(2+1+4+1+2)}$ x 5 x 19 x 9 x 17 x 15 x 7 x 13 x 3 x 11

x = $2^{10}$ x 5 x 19 x 9 x 17 x 15 x 7 x 13 x 3 x 11

Hence, the exponent of 2 in x is 10.