# Simplifying radicals(algebra II)

1. Feb 3, 2009

### liz777

1. The problem statement, all variables and given/known data

(cube root $$\sqrt[]{}x^4$$ * $$\sqrt[]{}x^5$$)^-2

Honestly, I tried and my answer didnt make any sense...The answer is supposed to be 1/(x^23/3)

How would I go about solving this? Any help would be appreciated :)

Also how would I solve the cube root of 7 * the cube root of 49?

2. Feb 3, 2009

### Staff: Mentor

What you wrote is very difficult to decipher. How about rewriting it using exponents rather than radicals? The cube root of a is a^(1/3).

The cube root of 7 times the cube root of 49 is the cube root of 343, which can be simplified.

3. Feb 3, 2009

### v0id19

Think about what you have: 2 cube roots. One is $$\sqrt[3]{7}$$ and the other is $$\sqrt[3]{7^2}$$. What can you do with that?

Last edited: Feb 3, 2009
4. Feb 3, 2009

### liz777

ok I get that one! you would get cube root of 7^3...so you would get 7. thanks I get that one now!

and back to the first problem. in exponents I think it would be:

(X3/4 * X1/5)-2

So if anyone wants to help with this one...so far I still have the wrong answer, I have no idea what I'm doing wrong!

5. Feb 3, 2009

### symbolipoint

Laws of Exponents are taught in Algebra 1 and Algebra 2.

a-m=$$\frac{1}{am}$$
That one did not type set correctly. I'm trying to state
'a' to the negative m power equals the fraction one over a to the m power. a^(-m)=1/(a^m)

aman=am+n

Last edited: Feb 3, 2009
6. Feb 3, 2009

### Staff: Mentor

That doesn't look like what you started with, which I think should look more like this:
(x4/3 * something)-2

The first factor inside the parentheses seems to be the cube root of x^4, which is x4/3. The other factor appears to be the square root of x^5. Can you tell us exactly what the problem is that you're working on?