How do you simplify #((3x^7)/2)^6(x^2)^6#?

2 Answers
sankarankalyanam
Jun 20, 2018

#color(purple)(=> (729/64)x^54#

Explanation:

https://revisionmaths.com/advanced-level-maths-revision/pure-maths/algebra/indices

#a^m * a^n = a^(m + n), (a^m)^n = a^(mn)#

#((3x^7)/2)^6 * (x^2)^6#

#=> (((3x^7) / 2)* x^2)^6#

#=> ((3x^9)/2)^6#

#=> (3^6 * x^(9*6)) / 2^6#

#color(purple)(=> (729/64)x^54#

Alan P.
Jun 20, 2018

#729/64 x^54#

Explanation:

In general #color(red)a^color(lime)p * color(blue)b^color(lime)p=(color(red)a * color(blue)b)^color(lime)p#

So
#color(white)("XXX")(color(red)((3x^7)/2))^color(lime)6 (color(blue)(x^2))^color(lime)(6)= ((color(red)(3x^7) * color(blue)(x^2))/color(red)2)^color(lime)6#

#color(white)("XXX")=((3x^9)/color(red)2)^color(lime)6#

#color(white)("XXX")=(3^6)/(2^6) x^(9 * 6)#

#color(white)("XXX")=729/64 x^54#

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