How do you simplify #((x^-3y^-8)/(x^4y^-2))^-7# and write it using only positive exponents?

1 Answer
Jun 2, 2017

Answer:

#((x^(-3)y^(-8))/(x^(4)y^(-2)))^(-7)# simplified is #color(blue)(x^(49)y^(42)#

See the process in the explanation.

Explanation:

Simplify:

#((x^(-3)y^(-8))/(x^(4)y^(-2)))^(-7)#

Apply the power rule of exponents: #(a^m)^n=a^(m*n)#.

#(x^(-3*-7)y^(-8*-7))/(x^(4*-7)y^(-2*-7))#

Simplify.

#(x^(21)y^(56))/(x^(-28)y^(14))#

Apply the quotient rule of exponents: #(a^m)/(a^n)=a^(m-n)#.

#x^((21)-(-28))y^(56-14)#

Simplify.

#x^(49)y^(42)#