Question

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

Answer 1

See the entire simplification process below:

Explanation:

First, to simplify the numerator we will rewrite this expression as:

`((2 * 3 * 4)(x^2 * x^2 * x)(y^4 * y^4))/(3x^-3y^2) -> (24(x^2 * x^2 * x)(y^4 * y^4))/(3x^-3y^2)`

We can now use these two rules for exponents to simplify the numerator:

`a = a^color(red)(1)` and `x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`(24(x^2 * x^2 * x^color(red)(1))(y^4 * y^4))/(3x^-3y^2) -> (24x^(2 + 2 + 1)y^(4+4))/(3x^-3y^2) -> (24x^5y^8)/(3x^-3y^2) ->`

`(8x^5y^8)/(x^-3y^2)`

We can now use this rule of exponents to complete the simplification:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`(8x^color(red)(5)y^color(red)(8))/(x^color(blue)(-3)y^color(blue)(2)) -> 8x^(color(red)(5)-color(blue)(-3))y^(color(red)(8)-color(blue)(2)) -> 8x^(color(red)(5)+color(blue)(3))y^(color(red)(8)-color(blue)(2)) ->`

`8x^8y^6`