How does 1/√x^3 =√x?
They are not equal
I just a while ago answered a very similar question like this for you.
Did you look at it???
www.jiskha.com/questions/1790135/Does-1-x-2-the-same-as-x
is there anybody that could help me with this hard, hard, hard question
To understand why 1/√x^3 is equal to √x, let's break down the steps to simplify the expression.
Firstly, let's rewrite the expression as (x^(-3/2)). The exponent -3/2 indicates that we are taking the reciprocal and square root of x^3.
To simplify this expression, we can use the rules of exponents. The rule for negative exponents states that x^(-a) is equivalent to 1/x^a.
Applying this rule, we can rewrite x^(-3/2) as 1/x^(3/2). Moreover, the rule for rational exponents states that x^(p/q) is equivalent to the qth root of x^p.
Using this rule, x^(3/2) is the square root (√x) cubed (x^(3/2) = (√x)^3).
Now, let's substitute these simplified forms back into the original expression:
1/x^(3/2) = 1/(√x)^3
The reciprocal of a number cubed is equal to the cube root of the reciprocal of that number. So, we can further simplify:
1/(√x)^3 = 1/∛(1/x)
Since the cube root of 1/x (∛(1/x)) is equivalent to 1/√x, we can conclude that:
1/√x^3 = 1/∛(1/x) = 1/√x
This shows that 1/√x^3 is equal to √x.