I need a step by step explanation/ answer plzzz
Simplify the following radical expression sqrt 72x^13y^11/8xy^13
√(72x^13y^11/8xy^13)
= √(72/8 x^13/x y^11/y^13)
= √(9x^12/y^2)
= 3x^6/y
Well, the first step is to simplify the numbers inside the square root. The square root of 72 can be simplified to 6√2, and the square root of 8 can be simplified to 2√2.
So now the expression is (6√2x^13y^11) / (2√2xy^13).
Next, simplify the variables. We can divide the x terms: x^13 / x = x^(13-1) = x^12.
Similarly, we can divide the y terms: y^11 / y^13 = y^(11-13) = y^-2.
Now our expression becomes (6√2x^12y^-2) / (2√2xy^13).
Next, simplify the square root terms: 6/2 = 3, and √2 / √2 = 1.
So our expression further simplifies to 3x^12y^-2 / xy^13.
Finally, simplify the y terms again: y^-2 / y^13 = y^(-2-13) = y^-15.
So the final simplified expression is 3x^12 / y^15.
Hope that helped! If you need any more humorously explained math problems, feel free to ask.
To simplify the radical expression, sqrt(72x^13y^11)/8xy^13, you can follow these steps:
Step 1: Rewrite the radical expression using the properties of radicals as a fraction:
sqrt(72x^13y^11) / 8xy^13
Step 2: Simplify the numerator by splitting the square root into individual factors:
sqrt(72) * sqrt(x^13) * sqrt(y^11)
Step 3: Simplify each individual factor within the square root:
sqrt(36 * 2) * sqrt(x^12 * x) * sqrt(y^10 * y)
Step 4: Further simplify within each square root:
6 * x^6 * y^5
Step 5: Combine the simplified factors within the square root:
6x^6y^5
Step 6: Rewrite the simplified radical expression as a fraction:
6x^6y^5 / 8xy^13
Step 7: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which in this case is 2:
(3x^6y^5) / (4y^12)
Step 8: Further simplify the expression:
3x^6 / 4y^7
Therefore, the simplified radical expression is 3x^6 / 4y^7.
To simplify the given radical expression, follow these steps:
Step 1: Simplify the coefficients under the radical sign
Take the square root of both the numerator and denominator separately:
√(72x^13y^11/8xy^13)
In the numerator:
√(72) is equal to √(36 * 2), which can be further simplified to 6√2.
In the denominator:
√(8) is equal to √(4 * 2), which simplifies to 2√2.
So the expression becomes:
(6√2x^13y^11)/(2√2xy^13)
Step 2: Simplify the variables
Since x and y are in both the numerator and the denominator, we can cancel them out:
(6√2x^13y^11)/(2√2xy^13) = (6√2x^(13-1)y^(11-13))/(2√2)
Simplifying the powers of x and y, the expression reduces to:
(6√2x^12y^(-2))/(2√2)
Step 3: Simplify the coefficient
Divide the numerator and denominator by 2:
(6√2x^12y^(-2))/(2√2) = (3√2x^12y^(-2))/(√2)
Simplifying further, we get:
(3x^12y^(-2))
So, the simplified expression is 3x^12y^(-2).