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 December 13th, 2016, 05:12 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 05:15 PM.
 December 13th, 2016, 05:18 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,979 Thanks: 1026 \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} Thanks from topsquark, deesuwalka and zekea
December 13th, 2016, 05:27 PM   #3
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 Originally Posted by romsek \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}
Oh wow thanks so much for the reply. One question I understand everything except for the 5^y * 3^y turns into (5*3) ^ y and then (15)^y

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, 05:31 PM   #4
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 Originally Posted by zekea Oh wow thanks so much for the reply. One question I understand everything except for the 5^y * 3^y turns into (5*3) ^ y and then (15)^y 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.
you are correct. If they are different bases you can't add the exponents together.

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, 05:13 AM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,195 Thanks: 872 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. Thanks from zekea
 December 14th, 2016, 05:36 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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