2 with exponent 3 over 2 with exponent 1...?

Question

2^3/2^1 (The numbers next to ^ are exponents) is equal to 2^2 or 4 in my algebra book. I know you have to subtract the exponents, leaving an exponent of 2, then divide the base...but that's where I'm having trouble. Why does it equal 2? Why not 1? 2 divided by 2 IS 1.

I would appreciate a thorough explanation, too. Thanks a lot!

PS This is written as a fraction, which you divide.

Answer 1

well an easy way to look at it is like this

(2*2*2)/(2)

now if u cancel out stuff it changes to this

(2*2)=4

or your way of doing it (subtracting exponents)

forget the first numbers for now and just look at the exponents

you have 3 and 1 subtracting those gets you 2 and 2^2=4 (because its 2*2=4) This leaves a 2^0 on bottom and anything to the 0 exponent is always equal to 1 so just before you finish your answer looks like this

2^2/1=4

Answer 2

When dividing, always subtract the powers if the numbers with the powers are equal. In this case both are the number 2 so that is fine. The answer is equal to 4.

2^3/2^1 = 2^(3-1) = 2^2 = 4

Answer 3

Once you subtract the exponents, you are left with:

2^2/2^0

2^2 is 4. 2^0 is 1 (any real non-zero number to the power of 0 is 1). So, you have:

4/1

Simplifying, you have 4.

Answer 4

you just subtract the exponents - no need to devide further
2^3/2^1 = 2^2 =4

or 8/2 = 4

exponents of the same base are devided by subtracting one from the other
5^3/5^2=5^1

Answer 5

When you subtract the exponents you then have 2^(3-1) which is 2^2=4
you don't divide the base, because they are the same base.
x^n/x^m=x^(n-m)

Answer 6

Rules of exponents. x^a/x^b = x^(a-b) so
2^3/2^1 = 2^(3-1) = 2^2 = 4

Doug

Answer 7

on top you have 2^3 on bottom you have 2^1
you just substract 3-1 = 2
so you have 2^2/2^0 = 2^2/1 = 4

you dont have to divide once more with the 2 at the bottom

Answer 8

2^3=8
2^1=2
so 8/2=4

Answer 9

???
u cancelled the exponent, leaving 2^2/1 isnt it?

Answer 10

2^3/2^1=2^2=4 answer