How do you simplify #(xy)^-3/(x^-5y)^3#?

1 Answer
May 3, 2016

Answer:

# = color(blue)(x ^12 y ^(-6)#

Explanation:

#(xy)^-3 / (x^-5 y)^3#

  • As per property:
    #color(blue)(a^m)^n = color(blue)(a^(mn)#

Applying the above property to the expression provided:

#(xy)^-3 / (x^-5 y)^3 = (x^ -3 y^-3) / (x^ ((-5 * 3) ) * y^3)#

# = (x^-3y^-3) / ((x^-15)* y^3#

  • As per property:
    #color(blue)(a^m / a^n = a^(m-n)#
    Applying the above to #x# and #y#:

# (x^-3y^-3) / (x^-15y^3)= x^ (-3 - (- 15)) * y ^ ((-3 -3))#

# = x ^ ((- 3 + 15 )) y ^(-6)#

# = x ^12 y ^(-6)#

  • As per property:
    #color(blue)(a^-1 = 1 /a#

# = x ^12 y ^(-6) = x ^12 / y ^6#