How do you simplify #(-2mn^2)^-3/(4m^-6 n^4)#?

1 Answer
Jun 16, 2015

Answer:

# = color(blue)(-m^3.n^-10)/32#

Explanation:

#(-2mn^2)^-3/(4m^-6 n^4)#

Simplifying the numerator:
#(-2^1m^1n^2)^color(red)(-3#
#=-2^(1 . color(red)(-3)) . m^(1. color(red)(-3)) . n^(2 . color(red)(-3)^#
# = -2^-3m^-3n^-6#
# = color(blue)(-1/2^3m^-3n^-6#
# = color(blue)(-m^-3n^-6)/8#

The expression can now be written as :
# = color(blue)(-m^-3n^-6)/(8.4m^-6 n^4)#

# = color(blue)(-m^-3n^-6)/(32m^-6 n^4)#

Note : #color(blue)(a^m /a^n = a^(m-n)#
Applying the above to the exponents of #m# and #n#

# = (-m^(-3+6).n^(-6-4))/32#
# = color(blue)(-m^3.n^-10)/32#