More important than 9 and 15 being factors of 45 is that 3 and 5 are factors of all three numbers: , 15= 3(5), and . So [tex](45)^{1/3}= ((3^2)(5))^{1/3}= (3^{2/3})(5^{1/3}), , and .
So .
Can you do it now?
1) Simplify:
I know I can split it up like below, but I'm finding it hard to remember where to go next.
It's obvious that both 9 and 15 are factors of 45, but, in terms of exponents, I can't remember the order of operations from here.
2) Simplify:
I know that a^(1/n) = nth root of a, but I can't seem to get the correct answer.
Thanks in advance.
If you are asking "How can I look at this problem and instantly know the answer without doing any calculation at all?", I can't help you because I certainly cannot do that. But in about the fourth or fifth grade I learned that to add fractions, you need to get a "common denominator". To add , you need the "common denominator" which, obviously, is . Multiplying both numerator and denominator of by gives
Note that answer is incorrect.
can be written as
But in general:
Have a look at this.