How do you simplify #(16xy)/(3x^5y^5)div (8x^2)/(9xy^7)#?

1 Answer
Jan 28, 2017

Answer:

#(16xy)/(3x^5y^5)-:(8x^2)/(9xy^7)=color(blue)((6y^3)/x^5)#

Explanation:

Simplify #(16xy)/(3x^5y^5)-:(8x^2)/(9xy^7)#

When dividing by a fraction, invert the fraction and multiply.

#(16xy)/(3x^5y^5)xx(9xy^7)/(8x^2)#

Simplify and group like terms.

#(144x^1xxx^1xxy^1xxy^7)/(24x^5xxx^2xxy^5)#

Apply product rule #a^m*a^n=a^(m+n)#

#(144x^(1+1)xxy^(1+7))/(24x^(5+2)xxy^5)#

Simplify.

#(6x^2y^8)/(x^7y^5)#

Apply quotient rule #a^m/a^n=a^(m-n)#.

#6x^(2-7)y^(8-5)#

Simplify.

#6x^(-5)y^3#

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

#(6y^3)/(x^5)#