SIMPLIFY: 3√(63x^5/(72y^6))
Example to enter answer: n√b, enter (b)^(1/n) Example: For 4√3:2, enter 4(2)^(1/3).What is my answer and how do i answer it?
3√(63x^5/(72y^6))
=3√9 √7 x^2 √x/(√36 √2 y^3)
= 9x^2√(7x) / (6√2 y^3)
= 3x^2 √(7x) / (2√2y^3)
they might now multiply top and bottom by √2 to rationalize the denominator to get
3x^2√(14x) / (4y^3)
check my work, I should have written it down first.
To simplify the expression 3√(63x^5/(72y^6)), we can break it down into smaller steps.
Step 1: Simplify the numerator and denominator separately.
We start by simplifying the numerator 63x^5 and the denominator 72y^6.
Step 2: Simplify the numerator.
To simplify 63x^5, we need to express it as a power of 3. Since 3 is a factor of 63, we can rewrite it as:
63 = 3 * 21
Now, let's simplify the variable part, x^5. We can rewrite it as:
x^5 = (x^3) * (x^2)
So, the numerator 63x^5 becomes:
63x^5 = 3 * 21 * (x^3) * (x^2)
Step 3: Simplify the denominator.
To simplify 72y^6, we follow a similar approach. Since 3 is a factor of 72, we can rewrite it as:
72 = 3 * 24
Now, let's simplify the variable part, y^6. We can rewrite it as:
y^6 = (y^3)^2
So, the denominator 72y^6 becomes:
72y^6 = 3 * 24 * (y^3)^2
Step 4: Combine the simplified numerator and denominator.
Now that we have simplified the numerator and denominator separately, we can rewrite the expression as:
3√((3 * 21 * (x^3) * (x^2)) / (3 * 24 * (y^3)^2))
Step 5: Simplify the expression inside the cube root.
We can cancel out the common factors of 3. The expression becomes:
3√((21 * (x^3) * (x^2)) / (24 * (y^3)^2))
Step 6: Simplify the expression further.
To simplify the expression inside the cube root, we can rewrite it as a power of 3:
(21 * (x^3) * (x^2)) / (24 * (y^3)^2) = ((21 * x^3 * x^2) / (24 * y^6))^(1/3)
So, the simplified expression is:
((21 * x^3 * x^2) / (24 * y^6))^(1/3)
To enter the answer, you would write it as:
(((21 * x^3 * x^2) / (24 * y^6))^(1/3))