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 * x6-3 * y3 = 4 * x3 * y3, which cannot be simplified further and is our final answer.
