How do you simplify expressions involving different powers?

Let's answer the question by solving an example:

Take (8x² * 5x⁴ * 2y³)/(20x³). Firstly, let's take a look at the first bracket and rearrange it so we have both numbers and variables grouped together:

= (8 * 5 * 2 * x² * x⁴ * y³)/(20x³). We can perform such operation because multiplication is commutative - the order does not matter.

= (80 * x² * x⁴ * y³)/(20x³). Secondly, to further simplify the expression in first brackets, we have to multiply x² and x⁴. To multiply powers of the same number (variable), we simply add the exponents (the "powers" or the numbers in index)

=(80 * x²⁺⁴ * y³)/(20x³) = (80x⁶ * y³)/(20x³) Now we can write this as a fraction and reduce it (80/20=4), so we are left with

= 4(x⁶ * y³)/(x³). Now, when dividing powers of the same number/variable, we, quite analogically to the previous example, substract one exponent from another to get:

= 4 * x^6-3 * y³ = 4 * x³ * y³, which cannot be simplified further and is our final answer.