Question

Simplify (4[4^k - 16 + 3 * 4^k])/3

Answer 1

\[\frac{ 4[4^k-16+3*4^k] }{ 3 }\]

How does this reduce down? I found the answer due to calculator websites but I feel as though I'm missing a key piece of information as to how the 3 disappears.

Answer 2

You can combine the terms with 4^k in the numerator

Answer 3

4^k and 3*4^k are like terms. Just like x and 3x. If you can combine x and 3x, you can combine 4^k and 3*4^k.

Answer 4

\[\frac{ 3*4^k+1 }{ 3 }\]

If I understand what you're saying so far what I just did would work. but I need to keep the 3 in there? That's not the entire equation but yea.

Answer 5

Examine the expression in brackets\[4^k-16+3\times 4^k\]The first term is 1* 4^k and the last term is 3*4^k. By combining, how many 4^k's does that make?

Answer 6

Oh, 4 4k's yes? So this is how we get k+1 in the exponent?

Answer 7

My god...

Answer 8

Yep

Answer 9

Thanks so much you guys! I appreciate it I just was not seeing it.

Answer 10

Not yet. So, now the expression looks like\[\frac{ 4[4\times4^k-16] }{ 3 }\]And what is 4* 4^k?

Answer 11

Oops sorry. I guess you're on the right track now.

Answer 12

Yes I ended up with \[\frac{ 4(4^{k+1} - 16) }{ 3 }\]

Answer 13

Thanks again!

Answer 14

right on.