cubed square root 16x^2y over cubed square root 2xy^2
I don't understand what you are saying
are you taking the cube root?
Why did the math book go to the comedy club? To find its square root and get a good laugh! But in all seriousness, to simplify the expression, we can simplify each term separately.
The cubed square root of 16x^2y can be simplified as follows:
cubed square root of 16 = 2
cubed square root of x^2 = x
cubed square root of y = y
So, the numerator simplifies to 2xy.
Similarly, the cubed square root of 2xy^2 can be simplified as:
cubed square root of 2 = √2
cubed square root of x = x
cubed square root of y^2 = y
So, the denominator simplifies to √2xy.
Therefore, the expression simplifies to (2xy) / (√2xy).
To simplify the expression (cubed square root 16x^2y / cubed square root 2xy^2), we can use the properties of radicals. The cube root of a number can be written as the number raised to the 1/3 power.
First, let's simplify the numerator:
cubed square root of 16x^2y = (16x^2y)^(1/3) = (2^4 * (x^2)^1 * y^1)^(1/3) = 2^(4/3) * x^(2/3) * y^(1/3) = 2 * x^(2/3) * y^(1/3).
Next, let's simplify the denominator:
cubed square root of 2xy^2 = (2xy^2)^(1/3) = 2^(1/3) * (x^1 * y^2)^(1/3) = 2^(1/3) * x^(1/3) * y^(2/3).
Now, let's divide the two simplified expressions to get the final simplified result:
(2 * x^(2/3) * y^(1/3)) / (2^(1/3) * x^(1/3) * y^(2/3))
= (2/2^(1/3)) * (x^(2/3 - 1/3)) * (y^(1/3 - 2/3))
= (2/2^(1/3)) * (x^(1/3)) * (y^(-1/3))
= 2^(3/3 - 1/3) * x^(1/3) * y^(-1/3)
= 2^(2/3) * x^(1/3) * (1/y)^(1/3)
= 2^(2/3) * x^(1/3) * (1/3)^(1/3).
So, the simplified expression is 2^(2/3) * x^(1/3) * (1/3)^(1/3), or in fractional form, 2^(2/3) * x^(1/3) * (1/3)^(1/3).
To simplify the expression (cubed square root 16x^2y) / (cubed square root 2xy^2), we need to simplify each term separately and then divide them.
Let's start by simplifying the numerator, which is the "cubed square root 16x^2y":
Step 1: Simplify the cubed square root of 16x^2y.
The cubed square root of a number is the same as raising that number to the power of 1/3. So, the cubed square root of 16x^2y can be written as (16x^2y)^(1/3).
Step 2: Simplify the expression within the parentheses.
Since 16 = 2^4, we can rewrite the expression as (2^4x^2y)^(1/3).
Step 3: Apply the exponent to each term within the parentheses.
When raising a power to a power, you multiply the exponents. So, (2^4x^2y)^(1/3) becomes 2^(4/3)x^(2/3)y^(1/3).
Now, let's simplify the denominator, which is the "cubed square root 2xy^2":
Step 1: Simplify the cubed square root of 2xy^2.
Similarly, the cubed square root of 2xy^2 can be written as (2xy^2)^(1/3).
Step 2: Simplify the expression within the parentheses.
Since we only have one term, (2xy^2)^(1/3) remains the same.
Now that we have simplified both the numerator and the denominator, we can divide them:
[(2^(4/3)x^(2/3)y^(1/3))] / [(2xy^2)^(1/3)]
To divide two terms with the same radical, we can subtract the exponents. So, the expression becomes:
2^(4/3 - 1/3)x^(2/3)y^(1/3) / 2^(1/3)x^(1/3)y^(2/3)
Simplifying further, we have:
2^(3/3)x^(1/3)y^(1/3) / 2^(1/3)x^(1/3)y^(2/3)
Cancelling out the common factors:
2^(3/3 - 1/3) * x^(1/3 - 1/3) * y^(1/3 - 2/3)
Finally, we simplify to get:
2 * x^0 * y^(-1/3)
Since any number raised to the power of 0 is equal to 1 and x^0 = 1, the expression further simplifies to:
2 * (1) * y^(-1/3)
And the final answer is:
2 * y^(-1/3), or 2/y^(1/3)