Question

the total numbers of prime factors of 512 to the power 9 is

Answer 1

I think it will help you....

Answer 2

Answer: 9

Step-by-step explanation:

Given number = $(512)^9$

When we find LCM of 512, we can see that $512=2\times2\times2\times2\times2\times2\times2\times2\times2\\\Rightarrow\ 512=2^9$

Now, $(512)^9=(2^9)^9=2^{9\times9}........\text{by law of exponent}(a^m)^n=a^{mn}\\\\\Rightarrow\ (512)^9=2^{81}$

Hence, there are 9 numbers of prime factors of  $(512)^9$