SOLUTION: 3y^29/11y^39 How do I simplify using only positive exponents?

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Question 1184524: 3y^29/11y^39
How do I simplify using only positive exponents?
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the 3 and the 11 stay put.
you have y%5E29%2Fy%5E39
move the 29 (the smaller) to the bottom subtracting 29 and leaving y^10 in the denominator.
3%2F11y%5E10. This is a positive exponent, as opposed to the equivalent (3/11)y^(-10)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.

https://mathinsight.org/exponentiation_basic_rules