Question

Help simplifying radical expressions?
I'll post a picture of the problem in the comments.

Answer 1

Remember these two properties of exponents.
Product of Powers Property: To multiply two powers having the same base, add the exponents.
Quotient of Powers Property: When you divide two powers with the same base, you subtract the exponents.
So in Francisco's expression, you'd subtract the fractions 1/2 and 3/18.
And in Ryan's expression, you'd add the exponents inside the root sign.
Also, recall that the exponent on the radicand can be turned into the numerator and the index can be turned into the denominator.

Answer 2

So Francisco's expression would be

Answer 3

or just x^1/3

Answer 4

Correct. :)

Answer 5

So I'm trying to make it not rational

Answer 6

?

Answer 7

what do you mean ?

Answer 8

I mean I don't want the fraction

Answer 9

you posted it
\[ \sqrt[3]{x} \]

Answer 10

You want the x^1/3 to look like

Answer 11

I just want to clarify

Answer 12

though these mean *exactly* the same thing \( \sqrt[3]{x} = x^\frac{1}{3} \)

Answer 13

Okay, you can put it either way. Whichever you are more comfortable using. Now, you only need to simplify Ryan's expression and check if it is equivalent to Francisco's. :)

Answer 14

the first way came first, then people realized it meant "fractional exponent", and now people use either way

Answer 15

Ryan's is also x^1/3 simplified from 9/27

Answer 16

Correct. ^.^

Answer 17

Thanks!

Answer 18

Sure :)