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

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Answer 1 · 2015-06-08T11:54:17

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

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

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

How do you simplify 3x²y * (4x^5 y)^-23x²y * (4x^5 y)^-2?