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Mathematics 11 Online
OpenStudy (anonymous):

w

OpenStudy (anonymous):

\[9^{1/3}*81^{1/3} \]

OpenStudy (anonymous):

I think it is 81 but the answer said it was 9, what am I doing wrong?

jimthompson5910 (jim_thompson5910):

\[\Large 9^{1/3}*81^{1/3}\] \[\Large 9^{1/3}*(9^2)^{1/3}\] \[\Large 9^{1/3}*9^{2*1/3}\] I'll let you finish up

OpenStudy (anonymous):

Sorry, I am only in 7th grad.. 9^1/3 is 3.

OpenStudy (anonymous):

But I am confused on the 9^2*1/3 part

jimthompson5910 (jim_thompson5910):

9^1/3 does NOT mean 9 times 1/3

jimthompson5910 (jim_thompson5910):

if we wanted to say " 9 times 1/3" we would write 9*1/3

OpenStudy (anonymous):

How do we do 9^1/3 then?

jimthompson5910 (jim_thompson5910):

\[\Large 9^{1/3}*9^{2*1/3}\] \[\Large 9^{1/3}*9^{2/3}\] now use the rule (a^b)*(a^c) = a^(b+c)

OpenStudy (anonymous):

hmm, so (9^1/3*9^2*1/3)= 9^1/3(9^2/3+c)?

jimthompson5910 (jim_thompson5910):

you add the exponents at this point

OpenStudy (anonymous):

so 9^1 because 1/3+2/3=1?

jimthompson5910 (jim_thompson5910):

yep, then 9^1 = 9

jimthompson5910 (jim_thompson5910):

anything to the first power is that number itself

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