Exponents and Roots Advanced

[Jenniferphillips270]

Hi, I am having difficulty understanding how the following is simplified. Does anyone have a few minutes to take a look and post a reply?

Question is from Chapter 12 of Number Properties 4th edition, pg 169

If 4^a + 4^a+1 = 4^a+2 - 176, what is the value of a

Answer is
176 = 4^a+2 -4^a - 4^a+1
176 = 4^a(4^2) - 4^a - 4^a*(4^1)

this is the part where i get stuck. The next line of the answer printed in the book is
176 = 4^a*(4^2 - 4^0 - 4^1)
I do not understand how the two "-4^a" from the second row become "-4^0"

Thank you for your help

[vvaibhav100]

You must remember that 4^a = 4^a * 1 = 4^a * 4^0

as (any number)^0 =1 and hence 4^0 = 1

So when you take out 4^a common in the equation it becomes

176 = 4^a*(4^2 - 4^0 - 4^1)

Hope this helps .

[Jenniferphillips270]

Thank you so much for your help, yes that makes sense

[jlucero]

Great explanation. Make sure any future questions about our Strategy Guides are in the Non-CAT Math subforum.

[Editor's Note: Moved to Manhattan GMAT Non-CAT Math.]