operations with exponents

**jazzyredsox5** · August 26th 2009, 04:43 PM

okay, um i simplified the problem and got it down to 6a^6/6a^3. i know to cancel out the 6 but can't i simplify a^6/a^3 to a^2 ??????

**QM deFuturo** · August 26th 2009, 04:51 PM

Originally Posted by jazzyredsox5

okay, um i simplified the problem and got it down to 6a^6/6a^3. i know to cancel out the 6 but can't i simplify a^6/a^3 to a^2 ??????

$\frac{a^6}{a^3} \neq a^2$

Why do you think the answer is $a^2$ ?

When you multiply or divide two terms with the same base (in your example you are dividing two terms, both of base "a", so they are the same) you will ADD or SUBTRACT the powers of the base. For division, which ever had the higher power (numerator or denominator) will be where the positive base ends up. That is, if m > n,

$\frac{a^m}{a^n} = a^{m-n}$

if m < n, then

$\frac{a^m}{a^n} = \frac{1}{a^{n-m}}$

**eXist** · August 26th 2009, 04:52 PM

Nope you can't go from $\frac{6a^6}{6a^3} \ne a^2$

In fact when you divide monomials you have to subtract the exponents, so:
$\frac{6a^6}{6a^3} = a^{6 - 3} = a^3$

**jazzyredsox5** · August 26th 2009, 04:56 PM

ohh okay thank you. i always think that because the base is the same that there would be a common factor if it was a numer rather than a variable...and you would be able to simplify the fraction......idk. but thanks again!

**QM deFuturo** · August 26th 2009, 05:03 PM

Originally Posted by jazzyredsox5

ohh okay thank you. i always think that because the base is the same that there would be a common factor if it was a numer rather than a variable...and you would be able to simplify the fraction......idk. but thanks again!

Well in a way, there is.

$\frac{a^6}{a^3} = \frac{a*a*a*a*a*a}{a*a*a}$

You can factor out three a's from the numerator and denominator, leaving you with

$\frac{a*a*a}{1}$

**HallsofIvy** · August 26th 2009, 05:05 PM

Another way to see this is to think of $\frac{a^6}{a^3}$ as $\frac{aaaaaa}{aaa}$ cancel. The three "a"s in the denominator cancel three "a"s in the numerator, leaving three: $\frac{a^6}{a^3}= \frac{aaaaaa}{aaa}= a^3$

Blast! QM deFuturo got in 2 minutes ahead of me!

**jazzyredsox5** · August 26th 2009, 05:11 PM

thanks to both! that's what i meant as in canceling them out i just didnt think of it in terms of variables. thanks this helps so much with my summer work!

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