The value of x y power 2/3 x-ypower3/2 divide square root of x y .squa...
Solution:
Given:
x y power 2/3 x - y power 3/2 ÷ square root of x y .square root x-y power 3 and 6
Steps to solve the given expression:
- First, we need to simplify the numerator and denominator separately.
- Then, we can simplify the expression by dividing the numerator by the denominator.
Simplifying the numerator:
x y power 2/3 x - y power 3/2
Let's simplify the expression using the laws of exponents.
x y power 2/3 x - y power 3/2 = x^1/3 y^2/3 x - y^3/2
Using the distributive property, we get:
x^4/3 y^2/3 - x^1/3 y^5/2
Now, we need to find a common denominator for the two terms in the numerator. The common denominator is x^4/3 y^5/3. So, we can rewrite the expression as:
x^4/3 y^2/3 * y^1/3/y^1/3 - x^1/3 y^5/2 * x^1/3/x^1/3
After simplifying, we get:
(x^2 y - x y^3) / (x^4/3 y^5/3)
Simplifying the denominator:
square root of x y .square root x-y power 3 and 6
Let's simplify the expression using the laws of exponents.
square root of x y .square root x-y power 3 and 6 = √(x y) * √(x-y)^3 * √(x-y)^6
Using the laws of exponents, we get:
(xy)^1/2 * (x-y)^9/2
Simplifying the expression:
Now, we can simplify the expression by dividing the numerator by the denominator.
[(x^2 y - x y^3) / (x^4/3 y^5/3)] / [(xy)^1/2 * (x-y)^9/2]
Using the laws of exponents, we can rewrite the expression as:
(x^2 y - x y^3) / (x^2/3 y^11/3 * (x-y)^9/2)
Therefore, the simplified expression is (x^2 y - x y^3) / (x^2/3 y^11/3 * (x-y)^9/2).
Final Answer:
The value of the expression is (