Question 1184524
your original equation is (3y^29)/(11y^39)


the parentheses need to be there to insure that 3y^29 is in the numerator and 11y^39 is in the denominator.


without the parentheses, 3y^29/11y^39 would be equal to 3y^29/11 * y^39 which gives you a different result.


the problem appears to be in the denominator.


without the parentheses, you are dividing by 11 and then multiplying by y^39.
with the parentheses, you are dividing by 11 * y^39.


bottom line:


parentheses ensure you are processing what you think you are processing with no nasty surprises at the end because of the order of mathematical processing logic.


(3y^29)/(11y^39) is equivalent to 3/11 * y^29/y^39


which is equivalent to 3/11 * y^(29-39)


which is equivalent to 3/11 * y^(-10)


which is equivalent to 3/11 * 1/y^10)


which is equivalent to 3/(11 * y^10)


which is equivalent to 3/(11y^10)


that should be your answer.


the laws of exponents tell you that x^-y is equal to 1/x^y


that's how you convert that minus exponent to a positive exponent.


here's a reference on exponent arithmetic.


<a href = "https://mathinsight.org/exponentiation_basic_rules" target = "_blank">https://mathinsight.org/exponentiation_basic_rules</a>