Question

How do you multiply and simplify `\frac { 3x ^ { - 3} y ^ { 3} \cdot 2y ^ { 4} } { 3x y ^ { - 4} }`?

Answer 1

`(3x^(-3)y^(3)*2y^4)/(3xy^(-4))=color(blue)((2y^11)/(x^4)`

See the process in the explanation.

Explanation:

Simplify:

`(3x^(-3)y^(3)*2y^4)/(3xy^(-4))`

Remove the multiplication symbol in front of `2y^4`. If you put the exponents inside parentheses, you won't need the multiplication symbol.

`(3x^(-3)y^(3)2y^4)/(3xy^(-4))`

Gather like terms.

`(2*3x^(-3)y^(3)y^4)/(3xy^(-4))`

Simplify.

`(6x^(-3)y^3y^4)/(3xy^(-4))`

Simplify.

`(2x^(-3)y^3y^4)/(xy^(-4))`

Apply the negative exponent rule: `a^-n=1/a^n`.

`(2y^3y^4y^4)/(x^(1)x^3)`

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

`(2y^(3+4+4))/(x^(1+3))`

Simplify.

`(2y^11)/(x^4)`