What is 12x^6 / 7 divided by 4x^2 / 5 ?

When dividing fractions, the first step is to change the division symbol to a multiplication symbol and flip the fraction that we are dividing by which gives us 12x⁶ / 7 multiplied by 5 / 4x². The next step is to cancel coefficients if possible by taking out common factors from the numerators and denominators. This isn't a necessary step but it makes the calculations easier later on in the question so is well worth doing! Here we can notice that 4 is a factor of both 4 and 12 so cancelling this gives us 3x⁶ / 7 multiplied by 5 / x². Next we need to cancel the variables. Here we can use the index rule for dividing powers which is x^a divided by x^b = x^a-b, so subtracting the indices of the powers of x will give us 3x⁴ / 7 multiplied by 5 / 1. Note that it's really tempting to divide the indices here but we need to remember not to do this! Finally we can write the calculation as a single fraction by multiplying the numerators together and multiplying the denominators together. This gives 3x⁴ multiplied by 5 as the numerator, which can be written as 15x⁴ as we just multiply the coefficients. The numerator will be 7 as anything multiplied by 1 doesn't change the number. Hence, we end up with an answer of 15x⁴ / 7.