Can anyone explain why 3^3/5 x 3^ 8/5 = 3^11/5 instead of 9^11/5

Question

Can anyone explain why 3^3/5   x    3^ 8/5 = 3^11/5 instead of 9^11/5

amistre64 · Answer

bases arent "numbers" in that sense

anonymous · Answer

because 8+3 = 11

anonymous · Answer

Because they are powers. When multiplying with powers you add the exponents.

amistre64 · Answer

they are symbols that represent another number

anonymous · Answer

for the same reason that 
$$10^2\times 10^3=10^5$$ and not 
$$10^2\times 10^3=100^5$$

amistre64 · Answer

3^2 = 9

4^3 = 64

amistre64 · Answer

the base is not a "number", its a representation of a number

anonymous · Answer

hmm

amistre64 · Answer

3^2 * 3^3 means:  (3*3)*(3*3*3) = (3*3*3*3*3) = 3^5

anonymous · Answer

Yeah I get that

amistre64 · Answer

as you can see; 3^5 doesnt mean 9^5 does it?

anonymous · Answer

yeah

anonymous · Answer

You know what. Just think of it this way, when you multiply powers, you don't ACTUALLY multiply all the numbers that are present. You just need to add the exponents. When you're dividing, just do subtraction with the exponents.

anonymous · Answer

So if I had 3^2/3   x   4^2/3 what would my answer be?

amistre64 · Answer

well, handwaving never amounts to understanding does it.

amistre64 · Answer

youd have no answer in that form; since they represent 2 unlike terms

anonymous · Answer

You have to have the same base number.

amistre64 · Answer

3 is not the same term as 4

amistre64 · Answer

you could still come to an answer; just not a shortcut answer :)

anonymous · Answer

so why can't you multiply the bases if the bases have exponents

amistre64 · Answer

we just established why.

amistre64 · Answer

3*3*3*3*3 not= 9*9*9*9*9 ...

amistre64 · Answer

the rules havent changed any fromthen til now :)

amistre64 · Answer

spose i develop a system of math that say RW$/ can add to *)♫i and produce any prime number i want

amistre64 · Answer

all that means is that I have established a rule that has a certain consequence and rests soley on the definition of the symbols

amistre64 · Answer

bases and exponents are just like that; there are only certain rules that will make them useful

anonymous · Answer

I think I see what you are saying, so if I had 3^2   x 4^3 I could not solve that until the exponents are gone

amistre64 · Answer

correct; or unless you could convert them in some fashion to like bases

anonymous · Answer

oh okay I think I get it now! Thank you guys!

amistre64 · Answer

youre welcome, and good luck :)

anonymous · Answer

What grade are you in?

anonymous · Answer

I'd rather not say lol...

anonymous · Answer

goodbye

anonymous · Answer

That's okay. hahaa.