Hi, I have a question regarding simplifying the following expression:
(1/x)/((1/3)x^(-2/3)) = 3/3sqrtx
The last expression reads three over cube root of x. I don't understand how to get from the expression on the left side of the equal sign to the one on the right.
Could somebody please help me out?
Your help would be greatly appreciated!
multiplying by 1/3
... (1/x) / [x^(-2/3)] = 1 / [x^(1/3)]
multiplying by x^(-2/3)
... 1/x = [x^(-2/3)] / [x^(1/3)]
... = 1 / [x^(3/3)] = 1/x
re-writing your equation:
(1/x)/((1/3)x^(-2/3)) = 3/x^(1/3)
(3/x) x^(2/3) = 3/ x^(1/3)
divide by 3
(1/x) x^(2/3) = 1/x^(1/3)
multiply both sides by x^(1/3)
(1/x)(x)^1 = 1
1 = 1
so the equation is true for all x, except of course x = 0, or else we would be dividing by zero
Thank you for your help, Scott and Reiny.
Sure! I'd be happy to help you understand how to simplify the expression.
To simplify the expression (1/x)/((1/3)x^(-2/3)), we can start by simplifying the nested fractions.
First, let's simplify the numerator of the expression (1/x). Since we have 1 over x, we can write this as x^(-1).
So now we have x^(-1)/((1/3)x^(-2/3)).
To divide by a fraction, we can multiply by its reciprocal. So we can rewrite the expression as x^(-1) * (3/(1x^(-2/3))).
Next, let's simplify the denominator of the expression (1x^(-2/3)). Since we have x raised to the power of (-2/3), we can rewrite it as 1/x^(2/3).
Now, our expression becomes x^(-1) * (3/(1/x^(2/3))).
Now, let's multiply the numerators and denominators together.
The numerator becomes x^(-1) * 3, which is just 3/x.
The denominator becomes 1/x^(2/3).
Now, our expression is simplified to 3/x / (1/x^(2/3)).
To divide by a fraction, we can multiply by its reciprocal again. So we can rewrite the expression as 3/x * (x^(2/3)/1).
Finally, we can simplify further by canceling out the x terms.
The x in the numerator and the x in the denominator cancel out, leaving us with 3 * x^(2/3).
Therefore, (1/x)/((1/3)x^(-2/3)) simplifies to 3 * x^(2/3), which can also be written as 3/∛x.
I hope this helps! Let me know if you have any further questions.