Question

How are rational exponents and radicals related? What procedures are followed to rewrite expressions involving radicals and rational exponents? please help me asap!! =[

Answer 1

Rational exponents:
\[x^\frac{ 1 }{ 2 }\] is the same as \[\sqrt{x}\]

The Numerator of the rational exponent is what power the variable or number etc. is being raised to, and the Denominator indicates what level of root you need to take of the variable, number, etc.

Answer 2

\[x^\frac{ 2 }{ 3 } = \sqrt[3]{x^2}\]

Answer 3

still kinda lost, can you explain it a little bit more? @wckeller

Answer 4

Lets say I have the variable X. I but I need to take the square root of x using rational exponents.

Instead of writing
\[\sqrt{x}\]
I would write \[x^\frac{1}{2}\]

The 2 in the denominator signifies that I am taking the 2nd root (also called the square root) of X.

The 1 in the numerator signifies that my variable X is being raised only to the first power.
Think about if i wrote \[x^\frac{2}{2}\]
It would really be \[x^1\] because \[\frac{2}{2} = 1\]

Answer 5

In my second example i forgot to add this...
\[\sqrt{x^2} = x^1 = x^\frac{ 2 }{ 2 }\]

Answer 6

okay i think i am getting it.. could you help me formulate it into words for a response?

Answer 7

Sure!

Rational exponents and radicals are related in the sense that rational exponents create radicals. A variable to the power of a rational number i.e. one-half, tells us that the radical is taking the number of the second root of that variable. The numerator tells us that the variable is only being put to the first power.

The procedures involved in rewriting radicals into rational exponents is simple. First take the root of the radical and put it in the denominator of the exponent, then take what the radicand's power is and put it in the numerator. The same steps are taken to rewrite rational exponents into radicals, but in reverse.

Answer 8

thank you dude, you're the man! :)