• liz777
In summary, the conversation is about simplifying the expression (cube root of x^4 times cube root of x^5)^-2, which simplifies to 1/(x23/3). The conversation also discusses using exponents instead of radicals and applying the laws of exponents. The second part of the conversation involves finding the cube root of 7 times the cube root of 49, which simplifies to the cube root of 343 or 7.
liz777

## Homework Statement

(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?

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.

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

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?

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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!

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:
liz777 said:
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!

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?

## 1. What is a radical expression?

A radical expression is an algebraic expression that contains a square root (√) or other higher roots. It is also known as a radical or a surd.

## 2. How do you simplify radical expressions?

To simplify a radical expression, you need to find the perfect square factors of the number under the radical sign and take their square root. You can then simplify any remaining factors outside the radical sign, if possible.

## 3. What is the difference between simplifying and solving radical expressions?

Simplifying a radical expression means reducing it to its simplest form, while solving a radical expression means finding the numerical value of the expression by solving for the variable.

## 4. Can radical expressions be negative?

Yes, radical expressions can be negative. However, they cannot have a negative number under the radical sign. This is because taking the square root of a negative number results in a complex number, which is not allowed in radical expressions.

## 5. What are some common mistakes to avoid when simplifying radical expressions?

Some common mistakes to avoid when simplifying radical expressions include forgetting to simplify perfect square factors, mixing up addition and multiplication rules, and not checking for extraneous solutions when solving radical equations.

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