# help understanding working with exponents

• Apr 25th 2013, 02:59 AM
Bhoona
help understanding working with exponents
I'm working from a book at the moment and in it there is a problem where you have to multiply two fractions. I don't need to show you the whole sum but there is a part of it that has \$\displaystyle (a^4-b^4)\$ and in order to diagonal cancel the fraction down you needed to know that you can change that to \$\displaystyle (a^2+b^2)(a^2-b^2)\$. But i don't know the rule that lets you do that.

I know that\$\displaystyle (a^2-b^2)=(a+b)(a-b)\$ but i still didn't know i could just apply it like that. Is there a rule or formula i can use that can solve things like this in the future?
• Apr 25th 2013, 03:06 AM
ibdutt
Re: help understanding working with exponents
You are right. Remember that a^4 = (a^2)^2
So you have ( a^4 - b^4 ) = (a^2)^2 - (b^2)^2 = ( a^2 + b^2) ( a^2 - b^2) = ( a^2 + b^2) ( a + b) ( a-b)
• Apr 25th 2013, 03:40 AM
Bhoona
Re: help understanding working with exponents
ahhh so \$\displaystyle (a^2)^2-(b^2)^2\$is a difference of squares also. I forgot you could split the exponent with brackets like that. That's the thing i was missing. Thank you.