Can anyone explain why... 2^2 x 2^5 = 128 and not 4^7 ... I dont get it..?

Since the bases are the same, you can just add the exponents. Just like x*x = x^2 or x^2*x = x^3.

2^2*2^5 = 2^7 =128

Or you could use the order of operations and handle the exponent of each part first.

2^2 =4
2^5=32
4*32=128

The bases remain unmultiplied. You only ADD the powers if the bases are the same. That's the rule.

a^m * a*n = a^(m + n) AND NOT a^2^(m + n)

So, 2^2 * 2^5 = 2^7 = 128.

I hope that helps. :)

me07.

No when you multiply x^m and x^n you get x^(m+n)

Example: Multiply 2^2 and 2^0 you get 2^(2+0) = 4 (not 4^2,which would be 16)

2^2 x 2^5 = 4 x 32 = 128

2^2 x 2^5
= (2 x 2) x (2 x 2 x 2 x 2 x 2)
= 2 x 2 x 2 x 2 x 2 x 2 x 2
= 2^2 x 2 x 2 x 2 x 2 x 2
= 2^3 x 2 x 2 x 2 x 2
= 2^4 x 2 x 2 x 2
= 2^5 x 2 x 2
= 2^6 x 2
= 2^7 (128)

RULE
---------
a^b x a^c = a^(b + c)

Thus

2^2 x 2^5 = 2^(2 + 5) = 2^7 = 128

When you multiply exponents you add them.
(2 ^ 2) * (2 ^ 5) = 2 ^ ( 5 + 2 ) = 2 ^ 7

When you divide exponents you subtract them.

2 ^ 5 / 2 ^ 3 = 2 ^ ( 5 - 3 ) = 2 ^ 2


-------------------------------------------------------

Now for another rule about grouping exponents...

If the base of a number is a multiple
( Example: 4 and 8 are multiples of 2)

Then the exponent gets divided by how many multiples are required to equal that base.

4 is 2^2,

Since 4 = 2 ^ 2, it talks 1/2 as much in the exponent to equal the same number.

For 8 it takes 1/3 as much since 2^3 = 8


Lets look at an example...

2^ 4 = 2 * 2 * 2 * 2 = 16
2^ 6 = 2 * 2 * 2 * 2 * 2 * 2 = 64

What we can expect is there only to be half as many 4's and a 3rd as many 8's.

Let's see...

4 ^ 2 = 4 * 4 = 16
4 ^ 3 = 4 * 4 * 4 = 64

Where it took four 2's to make 16 it only took two ( half as many) 4's.

To emphasize this, lets look at 64 broken down into groups of 2's

4 ^ 3 = (2 * 2) * (2 * 2) * (2 * 2) = 64

Again, It takes six 2's to equal 64 but only three 4's.

Does that make sense....

The same is true for the 8's, but its divided but it takes 1/3 less...

2^ 6 = 8 ^ 2 = 64 = (2 * 2) * (2 * 2) * (2 * 2)

No, but close. When the base is the same and you are dealing with numbers which have exponents, you can simply ADD (+) the exponents, but you leave the base the same

2^2 x 2^5 Is the same as 2^7

Let's examine why:

2^2 = 2x2

2^5= 2x2x2x2x2

Therefore, the two added together are 2x2x2x2x2x2x2, or 2^7, to which the result is 128.

I hope I clarified it for you,

QuestionMark

You cannot multiply bases and powers together like in division.

However you can do this:
(2^2) x (2^5)
=2 ^ (2+5)
= 2^7
= 128

That should do the trick... :)

No if you did that you'd be taking the terms apart. The exponents are not separate terms that can be moved about independently. The two squared is a number as is the two to the fifth. 4 x 32. What is a legal operation is to just add the exponents ( two to the seventh is 128 ). But this only works when the base numbers ares the same, in this case two. See the link below.