SOLUTION: Find the value of m if 3^3 times 9^3 times 27^3........times 19683^3= 3^m

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Question 1021021: Find the value of m if 3^3 times 9^3 times 27^3........times 19683^3= 3^m
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of m if 3^3 times 9^3 times 27^3........times 19683^3= 3^m
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-->
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3%5E%283%2B9%2B27%2B81%2B243%2B729%2B2187%2B6561%2B19683%29+=+3%5Em
--> m = 3+9+27+81+243+728+2187+6561+19683
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do the addition.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if 3%5E3%2A9%5E3%2A27%5E3*........*+19683%5E3=+3%5Em+
we can write it like
3%5E3+%2A+3%5E6+%2A3%5E9*........*19683%5E3=+3%5Em
factor 19683
19683+=+3%5E9
so we have
19683%5E3=%283%5E9%29%5E3+=3%5E27
as you can see here 3%5E3+%2A+3%5E6+%2A3%5E9, each next multiplier has exponent 3 more than previous one, so write all of them up to 3%5E27
3%5E3+%2A+3%5E6+%2A3%5E9%2A3%5E12%2A3%5E15%2A3%5E18%2A3%5E21%2A3%5E24%2A3%5E27=3%5Em...use the rule: if base is same,add exponents
3%5E%283+%2B6+%2B9%2B12%2B15%2B18%2B21%2B24%2B27%29=3%5Em
3%5E%28135%29=3%5Em
so, m=135