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simplifying numbers with exponents

kjdjean

New member
Joined
Jan 18, 2010
Messages
2
how do I simplify:

3 to the 10th power plus 3 to the 10th power plus 3 to the 10th power ??
 

chrisr

Full Member
Joined
Nov 29, 2009
Messages
355
\(\displaystyle 3^{10}+3^{10}+3^{10}=(3)3^{10}=3^13^{10}=3^{1+10}=3^{11}\)
 

kjdjean

New member
Joined
Jan 18, 2010
Messages
2
Thank you! You are the first of many that I have asked that showed me how to get the right answer.
 

chrisr

Full Member
Joined
Nov 29, 2009
Messages
355
It's based on the following.

The exponent is the number of three's that are multiplied together.

\(\displaystyle 3(3)3(3)=3^4\)

\(\displaystyle 3(3)=3^2\)

\(\displaystyle 3(3)3(3)3=3^5\)

When multiplying, we just line up all the three's.

\(\displaystyle 3^43^3=[3(3)3(3)][3(3)3]=3(3)3(3)3(3)3=3^7=3^{4+3}\)

the same strategy for other powers, or you could replace all the three's with another repeating number

\(\displaystyle 5^25^7=5^{2+7}=5^9\)

In your example, adding 3 of the same thing is multiplying it by 3.

\(\displaystyle 2+2+2=3(2)\ etc\)
 
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