Exponents

[m_blooms]

5^21 * 4^11 = 2 * 10 ^n

What is the value of n?

[Sakhalin]

I think the answer for n=21

5^21*4^11=2*10^n
5^21*2^22=2*5^n*2^n
Threfore n must equal 21

I am not sure. Please let me know if you know the correct solution

[Sakhalin]

I think the answer for n=21

5^21*4^11=2*10^n
5^21*2^22=2*5^n*2^n
Threfore n must equal 21

I am not sure. Please let me know if you know the correct solution

[VP_RedSoxFan]

The only way to solve this one is to realize what the exponents really mean.

You can think of 5^21 as a list of 21 5's multiplied together.

4^11 = (2^2)^11 = 2^22 and you can think of this as a list of 22 2's multiplied together.

Instead of multiplying the all of the 5's and then all of the 2's, then multiplying their products together, you can match up a 5 and 2. Now instead of 21 5's and 22 2's, you have 21 10's and a 2 to multiply together. And, clearly, another way to write that would be 2 * 10^21

The answer is 21

[AleksandrM]

I got 21 as well. The key in this one is to see that when you split 10^n the result is not 2 * 5^n but is 2^n * 5^n. Another mistake that could be made is to ignore the 2 and forget that it is 2^1, leaving a 1 behind.