Find out the no of digits in product between some prime.

Question

How many digits are there in? $2^{17}*3^{2}*5^{14}*7$. help me.

Answer 1

As André Nicolas has pointed out in the comments,

$$2^{17}\times 5^{14} = 2^3\times 2^{14}\times 5^{14} = 2^3\times 10^{14} = 8\times 10^{14}.$$

Therefore,

$$2^{17}\times 3^2\times 5^{14}\times 7 = 3^2\times 7\times 8\times 10^{14} = 504\times 10^{14} = 5.04\times 10^{16}.$$

So $2^{17}\times 3^2\times 5^{14}\times 7$ has $17$ digits.