Question

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

Answer 1

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

Explanation:

`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`

Answer 2

`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`