%5E1%2F2(27x%5E6y%5E3%2F2)%5E1%2F3.jpeg "(49x^2y)^1/2(27x^6y^3/2)^1/3")
Simplifying the Expression: (49x^2y)^1/2(27x^6y^3/2)^1/3
In this article, we will simplify the expression (49x^2y)^1/2(27x^6y^3/2)^1/3. To do this, we will use the laws of exponents and some algebraic manipulations.
Step 1: Simplify the First Factor
Let's start by simplifying the first factor: (49x^2y)^1/2. We can rewrite this expression as:
(49x^2y)^1/2 = (7^2x^2y)^1/2
Using the law of exponents that states a^(mn) = (a^m)^n, we can rewrite the expression as:
(7^2x^2y)^1/2 = (7^2)^1/2(x^2y)^1/2
= 7^1(x^1y^1/2)
= 7x(y^1/2)
So, the first factor simplifies to 7x(y^1/2).
Step 2: Simplify the Second Factor
Now, let's simplify the second factor: (27x^6y^3/2)^1/3. We can rewrite this expression as:
(27x^6y^3/2)^1/3 = (3^3x^6y^3/2)^1/3
Using the law of exponents that states a^(mn) = (a^m)^n, we can rewrite the expression as:
(3^3x^6y^3/2)^1/3 = (3^3)^1/3(x^6y^3/2)^1/3
= 3x^2y(y^-1/2)
So, the second factor simplifies to 3x^2y(y^-1/2).
Step 3: Multiply the Two Factors
Now that we have simplified both factors, we can multiply them together:
(7x(y^1/2))(3x^2y(y^-1/2))
= 21x^3y(y^1/2)(y^-1/2)
= 21x^3y
And that's the final simplified expression!
