SOLUTION: what is the value of 2 to 6th power times 2 to the 4th power divided by 2 to the 5th power i know its 32 but i wanna know why its 32 ?

Algebra ->  Exponents -> SOLUTION: what is the value of 2 to 6th power times 2 to the 4th power divided by 2 to the 5th power i know its 32 but i wanna know why its 32 ?      Log On


   

Question 852674: what is the value of 2 to 6th power times 2 to the 4th power divided by 2 to the 5th power
i know its 32 but i wanna know why its 32 ?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here are some common exponent rules


(Image Source: http://coxmath.blogspot.com/2010/08/exponent-rules.html)


We will be using rule #1 and rule #2. You will use other rules for other problems, but we will only use those 2 rules for now.


%282%5E6%2A2%5E4%29%2F%282%5E5%29


%282%5E%286%2B4%29%29%2F%282%5E5%29 Using rule #1


%282%5E%2810%29%29%2F%282%5E5%29


2%5E%285%29 Using rule #2


32 Note: 2%5E5+=+2%2A2%2A2%2A2%2A2+=+32 (there are 5 copies of '2' being multiplied to get 32)


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So that's how %282%5E6%2A2%5E4%29%2F%282%5E5%29+=+32

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+2%5E6+%2A+2%5E4+%29+%2F+2%5E5+
As long as the base is the same ( 2 in this case ),
Multiplying ADDS the exponents
Dividing SUBTRACTS the exponents
-----------------------------------
To see this, just write everything out the long way:
+%28%28+2%2A2%2A2%2A2%2A2%2A2+%29%2A%28+2%2A2%2A2%2A2+%29%29+%2F+%28+2%2A2%2A2%2A2%2A2+%29+
-------------------------------------------------------
Now rewrite it this way:
+%28%28+2%2A2%2A2%2A2%2A2+%29%2A%28+2%2A2%2A2%2A2%2A2+%29%29+%2F+%28+2%2A2%2A2%2A2%2A2+%29+
It's the exact same thing, but now you can see the
cancellation top and bottom. You are left with:
+2%2A2%2A2%2A2%2A2+
----------------------
Expressed with exponents, what I just did was:
+%28+2%5E6+%2A+2%5E4+%29+%2F+2%5E5+
-------------------------------
+%28+2%5E5+%2A+2%5E5+%29+%2F+2%5E5+
-------------------------------
+2%5E5+
-------------------------------
And what I just did to get the final exponent = +5+ is
+6+%2B+4+-+5+=+5+
or, the same thing in the 2nd step:
+5+%2B+5+-+5+=+5+
------------------------
Just write everything down the long way if you get
confused, and do the top and bottom cancellation.
Hope this helps