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

1 Answer
Mar 12, 2018

Answer:

#((x^4y^(-7))/(x^(-2)y^4))^2=color(blue)(x^12/y^22#

Explanation:

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

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

#(x^(4-(-2))y^(-7-4))^2#

Simplify.

#(x^(4+2)y^(-11))^2=#

#(x^(6)y^(-11))^2#

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

#(x^(6*2)y^(-11*2))#

Simplify.

#x^12y^(-22)#

Apply negative exponent rule: #a^(-m)=1/a^m#

#x^12xx1/y^22#

Simplify.

#x^12/y^22#