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

1 Answer
May 4, 2017

Answer:

#(2y^3*3xy^3)/(3x^2y^4)=color(blue)((2y^2)/x)#

Explanation:

Simplify:

#(2y^3*3xy^3)/(3x^2y^4)#

Gather like terms.

#(2*3xy^3y^3)/(3x^2y^4)#

Divide whole numbers.

#(6xy^3y^3)/(3x^2y^4)#

Simplify.

#(2xy^3y^3)/(x^2y^4)#

Apply the product rule of exponents: #a^m*a^n=a^(m+n)#

#(2xy^(3+3))/(x^2y^4)#

Simplify.

#(2xy^6)/(x^2y^4)#

Apply the quotient rule of exponents: #"a^m/a^n=a^(m-n)# Recall that a variable without an exponent is understood to be raised to the 1st power.

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

Simplify.

#2x^(-1)y^(2)#

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

#(2y^2)/x#