Question

How do you simplify `3x²y * (4x^5 y)^-2`?

Answer 1

`(3x^²y) * (4x^5 y)^color(red)(-2`
`=(3x²y) * (4^color(red)(-2) . x^(5 . color(red)((-2))). y^color(red)(-2))`
`=(3x²y) * (4^-2 x^(-10)y^(-2))`

note: `color(blue)(a^m.a^n = a^(m+n)`

Applying the above property to the exponents of `color(blue)(x and y`

`=(3.4^-2) . color(blue)(x^(2+(-10)) . y^(1+(-2))`
`=(3.4^-2) . color(blue)(x^-8 . y^-1`

note: `color(blue)(4^-2 = 1/4^2 = 1/16`

`=color(blue)(3/16x^-8y^(-1)`