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December 13th, 2016, 06:12 PM   #1
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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.
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December 13th, 2016, 06:18 PM   #2
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$\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}$
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December 13th, 2016, 06:27 PM   #3
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Quote:
Originally Posted by romsek View Post
$\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.
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December 13th, 2016, 06:31 PM   #4
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Quote:
Originally Posted by zekea View Post
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.

$(a^c b^c) = (ab)^c$
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December 14th, 2016, 06:13 AM   #5
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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.
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December 14th, 2016, 06:36 AM   #6
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Ah, that's much clearer now. Thanks both of you guys!
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