Question

How do you simplify `((6x^4y^8)^3)/(4x^4y^10)`?

Answer 1

`54x^8y^14`

Explanation:

`((6x^4y^8)^3)/(4x^4y^10)`

`color(white)("XXX")=6^3/4 * ((x^4)^3)/(x^4) * ((y^8)^3)/(y^10)`

`color(white)("XXX")=(6*cancel(6)^3*cancel(6)^3)/(cancel(4)_(cancel(2)_1)) * (x^4)^2/1 * (y^24)/y^10`

`color(white)("XXX")=54x^8y^14`

Answer 2

`54x^8y^14`

Explanation:

Write as `(6^3xxx^(4xx3)xxy^(8xx3))/(4xxx^4xxy^10)`

`=> 216/4 xx x^12/x^4xxy^24/y^10`

`=> 54x^8y^14`

Answer 3

`54x^8y^14`

Explanation:

`color(blue)((6x^4y^8)^3/(4x^4y^10)`

First simplify `(6x^4y^8)^3`

Use the exponental property

`color(brown)((xy)^z=x^zy^z`

So,

`rarr(6x^4y^8)^3=(6x^4)^3(y^8)^3`

Remember

`color(purple)((6x^4)^3=(6x^4)(6x^4)(6x^4)`

`color(purple)((y^8)^3=(y^8)(y^8)(y^8)`

`rarr216x^12y^24`

Then solve for the question

`rarr(216x^12y^24)/(4x^4y^10)`

And also remind that

`color(brown)(x^y/x^z=x^(y-z)`

`rarr(cancel216^54x^cancel12y^cancel24)/(cancel4^1x^cancel4y^cancel10)`

`color(green)(rArr54x^8y^14`

Answer 4

`54x^8y^14`

Explanation:

Using the following `color(blue)" rules of exponents "`

`• (a^m)^n = a^(mxxn) = a^(mn)`

`• (a^m b^p)^n = a^(mn) b^(pn) " etc. "`

hence: `(6x^4y^8) = 6^(1xx3)x^(4xx3)y^(8xx3) = 6^3x^12y^24 =216x^12y^24`
`"-------------------------------------------------------------------"`
`• (a^m)/(a^n) = a^(m-n)`
`"----------------------------------------------------------"`

hence: `(216x^12y^24)/(4x^4y^10)`

`= 216/4 xxx^12 /x^4 xxy^24/y^10 = 54xxx^(12-4)xxy^(24-10)`

`= 54x^8y^14`