December 13th, 2016, 06:12 PM  #1 
Newbie Joined: Dec 2016 From: Canada Posts: 12 Thanks: 0  Exponential Expression
Combine and Simplify (3*5^y)(5*3^y) I'm a little confused here because you can't combine as they are different bases correct? Last edited by zekea; December 13th, 2016 at 06:15 PM. 
December 13th, 2016, 06:18 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816 
$\begin{align}&(3 \cdot 5^y)(5\cdot 3^y) = \\ &3\cdot 5 \cdot 5^y \cdot 3^y = \\ &15 \cdot (5\cdot 3)^y =\\ &15(15)^y =\\ &(15)^{y+1}\end{align}$ 
December 13th, 2016, 06:27 PM  #3  
Newbie Joined: Dec 2016 From: Canada Posts: 12 Thanks: 0  Quote:
I wasn't aware you were allowed to do that and then because the exponent is now outside the bracket it's okay to multiply the 3 and the 5. In the first step with the 5^y multiply 3^y I was like where do I go with this. They're different bases and therefore can't add the exponents together.  
December 13th, 2016, 06:31 PM  #4  
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,602 Thanks: 816  Quote:
However here we have a common exponent so we can group the bases with multiplication and raise the product to the common exponent. $(a^c b^c) = (ab)^c$  
December 14th, 2016, 06:13 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,821 Thanks: 750 
a^m means "a multiplied by itself , times" and b^m means "b multiplied by itself m times. For example a^4b^4= (a*a*a*a)(b*b*b*b)= a*a*a*a*b*b*b*b (because multiplication is associative) and then is equal to a*b*a*b*a*b*a*b (because multiplication is commutative) so is equal to (a*b)(a*b)(a*b)(a*b)= (ab)^4.

December 14th, 2016, 06:36 AM  #6 
Newbie Joined: Dec 2016 From: Canada Posts: 12 Thanks: 0 
Ah, that's much clearer now. Thanks both of you guys!


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