How do you simplify #(x^-1y^-2z^3)^-2 (x^2y^-4z^6)#?

1 Answer
Mar 15, 2016

Answer:

Use the following three properties:

#(x*y*z*...)^a=x^a*y^a*z^a*...#

#(x^a)^b=x^(a*b)#

#x^a*x^b=x^(a+b)#

Answer is:

#x^4y^0z^0#

Explanation:

#(x^-1y^-2z^3)^-2(x^2y^-4z^6)#

  • Use #(x*y*z*...)^a=x^a*y^a*z^a*...#

#(x^-1)^-2(y^-2)^-2(z^3)^-2x^2y^-4z^6#

  • Use #(x^a)^b=x^(a*b)#

#x^(-1*(-2))y^(-2*(-2))z^(3*(-2))x^2y^-4z^6#

#x^2y^4z^-6x^2y^-4z^6#

  • Use #x^a*x^b=x^(a+b)#

#x^(2+2)y^(4+(-4))z^(-6+6)#

#x^4y^0z^0#

Note: don't say that #y^0=1# and #z^0=1# because that is not true for #y=0# and #z=0#

If you wish you can use #x^-a=1/x^a# but it's easier without it.