Question

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

Answer 1

First, rewrite the numerator and use this rule for exponents to simplify the numerator:

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

`(x^color(red)(3) * x^color(blue)(3) * y^3)/(4x^2) = (x^(color(red)(3) +color(blue)(3)) * y^3)/(4x^2) = (x^6y^3)/(4x^2)`

Now, we can use this rule for exponents to simplify the `x` terms in the numerator and denominator:

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

`(x^color(red)(6)y^3)/(4x^color(blue)(2)) = (x^(color(red)(6)-color(blue)(2))y^3)/4 = (x^4y^3)/4`