Yes, it is embarrassing…my daughter needs help with her Algebra I homework and I can’t help. I don’t remember how to do it (I wasn’t that great at math myself) and I can’t decipher the example problems in her book. I don’t want to give her the answer, I just need a reminder how to work the problems so I can work with her. They are working on exponential equations. One of the example problems is:
Simplify (81^1/4)^-2 (81 to the one-fourth, to the negative 2) They are supposed to write it in radical form?
Can someone explain this at the most basic level so I can help her?
You multiply exponents.
(81^1/4)^-2 = 81^-1/2
A negative exponent is the inverse of the positive exponent
81^-1/2 = 1/81^1/2
Fractional exponents are roots
1/81^1/2 = 1/sqrt(81)
use the radical sign for sqrt
or, 1/9
Thanks! I think I can follow that…
81^1/4 means the cube root of 81, which is 3 ( 3x3x3x3 = 81).
3^-2 means 1/(3^2), or 1/9
What you described is the fourth root, not cube root.
Sorry, been a long time. How can 1/9 be represented as a radical? Would the square rot of 1/81 be correct or is there a fancier way?
You got the answer right, you just called it the wrong thing. “Cube root” is x^(-1/3), not x^(-1/4).
Thinks of x^2 is “x squared” and x^3 is “x cubed”.
Great! But, the real question is can your daughter follow it? That is the whole point of the exercise.
Pay no attention to that man behind that curtain. 
I agree, but if I can’t understand the reply, I can’t explain it to my daughter. I did understand and was able to help her, but then we got stuck on other problems. She’s going to ask her teacher to go over it again with her today in class.
Thanks everyone for the explanations!