Simple math question

Posterguy · January 16, 2014, 2:27pm

is 8^(k)

the same as

2^(3+k)

or

2^(3k)

thanks

allyphoe · January 16, 2014, 3:21pm

Try and solve it using logic, because logic can save you on the test, even if memory fails…

You need 3 2s in your multiplication string for every 8, right? (2^3 = 8)

So if you have k 8s in the string, and is takes 3 2s to make an 8, then 3k 2s is the same as k 8s.

Alternatively, solve for the simplest case, where k=0.

8^0 = 1

2^(3*0) = 2^0 = 1

2^(3+0) = 2^3 = 8

DrSteve · January 16, 2014, 4:35pm

Since 8=2^3, we have 8^k=(2^3)^k = 2^(3k)

Here I have used the law (a^b)^c = a^(bc)

2^(3+k) = (2^3)(2^k) = 8(2^k)

Posterguy · January 16, 2014, 4:41pm

Thanks for the explanations