I think that the goal is to get rid of the 5th root in this case. I know that I have to make whatever is under or in the root -in this case the number is X equal some number to the fifth power.
I am supposed to use the rule
a^(m/n)= n
(the n-root) (don't know how to type it) and under the root symbol a^m
and the other rule is (a^x)(a^b)= a^(x+b)
The book calls this Radical Ecponents and Radical Expretions.
My problem is that it only says X, another problem I had, I can solve
(I will use ,- to symbolise the root)
to give you an idea on another problem how this is supposed to be solved
[y^ (-1/4)][y(3/4)] (multiply the two terms)
Following the rule
4,- [y^(-1)][y^3] (the for stands for the 4th root and the rest is under the root symbol)
using the rule of multiplication of the powers you then get
4,- y^2
which is the same as the following and keeping in mind that there has to be some number to the power of 4.
4,- (y^(1/2)^4)
The fours cancel and then you have y^ (1/2)
Note that (1/2)4 is the same thing as 2 so it's like factoring too.
I just can't do the problem I showed you. I hope I gave you enough info to help me out!!
Thanks you!
(Original question below)
Please read and then help me!
(x^(-3/5))
----------- divide
x ^ (1/5)
I know the problem then needs to look like this:
(x^(-3/5))(x^(-1/5))
(multiply the two above)
Then it needs to look like this:
(I can't write it though, so I'll tell you)
The 5th root out of (x^(-3)(x^(-1)
Then that adds up to the 5th root out of x^(-4)
and this is were I need help. To get rid of the fifth root there neeeds to be something to the power of 5 under the root symbol, but how do I get there? If my math to this point isn't correct, please correct it. I need Help!
I thought I had answered your question before.
Your original expression of
(x^(-3/5))
----------- divide
x ^ (1/5)
reduces or can be simplified to x^(-4/5)
Other than writing this in several different forms such as (x^-4)^(1/5) or (1/x^4)^(1/5)
there is no need or no method to "get rid of" the fifth power unless you have a value for x
If you had an equation containing that expression there would be ways to solve for x by manipulating the fifth power using power rules.
To simplify the expression (x^(-3/5))/(x^(1/5)), we can use the rule for dividing exponents. This rule states that when dividing powers with the same base, we subtract the exponents.
In this case, we have x^(-3/5) divided by x^(1/5), which means we need to subtract the exponents: (-3/5) - (1/5) = -4/5.
Therefore, the simplified expression is x^(-4/5).
To illustrate this further, let's say we have a specific value for x, such as x = 2. We can substitute this value into our simplified expression: 2^(-4/5).
To evaluate this, we can use the rule for fractional exponents that states x^(m/n) = (n-th root of x)^m.
So, in this case, 2^(-4/5) can be written as (5-th root of 2)^(-4).
The fifth root of 2 is approximately 1.1487.
Therefore, (5-th root of 2)^(-4) ≈ (1.1487)^(-4) ≈ 0.485.
So, if x = 2, then the expression (x^(-3/5))/(x^(1/5)) simplifies to approximately 0.485.
However, if you do not have a specific value for x, you cannot simplify the expression any further without additional information or an equation to solve.