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9^3k * 27^3k-1 * 3^k  all divided by 81^4k  like a fraction

Solve the variable

SHOW ALL WORK

(Doin gr8 Cphill)

 Jan 17, 2017

Best Answer 

 #1
avatar+118687 
+15

9^3k * 27^3k-1 * 3^k  all divided by 81^4k  like a fraction

 

\(\;\;\;\frac{9^{3k} * 27^{3k-1} * 3^k }{ 81^{4k} }\\ =\frac{3^{2*3k} * 3^{3(3k-1)} * 3^k }{ 3^{4*4k} }\\ =\frac{3^{6k} * 3^{9k-3} * 3^k }{ 3^{16k} }\\ =3^{6k+9k-3+k-16k}\\ =3^{-3}\\ =\frac{1}{3^3}\\ =\frac{1}{27}\)

 Jan 18, 2017
 #1
avatar+118687 
+15
Best Answer

9^3k * 27^3k-1 * 3^k  all divided by 81^4k  like a fraction

 

\(\;\;\;\frac{9^{3k} * 27^{3k-1} * 3^k }{ 81^{4k} }\\ =\frac{3^{2*3k} * 3^{3(3k-1)} * 3^k }{ 3^{4*4k} }\\ =\frac{3^{6k} * 3^{9k-3} * 3^k }{ 3^{16k} }\\ =3^{6k+9k-3+k-16k}\\ =3^{-3}\\ =\frac{1}{3^3}\\ =\frac{1}{27}\)

Melody Jan 18, 2017
 #2
avatar+129899 
+10

[9^(3k) * 27^(3k-1) * 3^k] /   81^(4k)

 

[ (3^2)^(3k) * (3^3)^(3k - 1) * 3^k] / [3^4]^{4k)

 

[ 3^(6k) * (3)^(9k - 3) * 3^k ]  / [3^16]^k

 

[  3^ ( 6k + 9k - 3 + k ) ] / [3^(16k)]

 

[ 3^(16k - 3) ] / [3^ (16k)]

 

3^(16k - 3 - 16k)  =

 

3^( -3 )

 

1 / 27

 

 

 

cool cool cool

 Jan 18, 2017
 #3
avatar+129899 
+10

Rats  !!!.....Melody beat me to it.....!!!!!

 

 

 

cool cool cool

 Jan 18, 2017
 #4
avatar+118687 
+10

Now Chris,

You would have seen me working on it before you even started your answer :/

 Jan 18, 2017
 #5
avatar+129899 
+10

Nah.....I think you "stealth" posted it.....LOL!!!!!!

 

 

 

 

 

cool cool cool

 Jan 18, 2017
 #6
avatar+118687 
+10

Yeah right :/

 

Melody  Jan 18, 2017
 #7
avatar+234 
0

Is this a math or a drama website?

 Jan 18, 2017

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