Simplify the following expression:(6 x^4)(4 y^2) / [ (3 x^2)(16 y) ]
Please help, I don't get this!
(24/48)(x^4/x^2) (y^2/y)
(1/2) x^2 y
just add powers in products, and subtract in divisions:
(6x^4)(4y^2) / [(3x^2)(16y)]
= (6*4)/(3*16) * x^(4-2) * y^(2-1)
= 1/2 x^2 y
= x^2y/2
To simplify the given expression, we can follow these steps:
Step 1: Multiply the numbers in the numerator (6 and 4) and denominator (3 and 16):
(6 x^4)(4 y^2) = 24x^4y^2
(3 x^2)(16 y) = 48x^2y
So, the expression becomes: 24x^4y^2 / 48x^2y
Step 2: Simplify the variables by dividing the like terms. In this case, we can divide the common variables x and y:
24x^4y^2 / 48x^2y = (24/48) * (x^4/x^2) * (y^2/y)
Step 3: Simplify the resulting expression:
(24/48) = 1/2
x^4/x^2 = x^(4-2) = x^2
y^2/y = y^(2-1) = y
Therefore, the simplified expression is: (1/2) * x^2 * y
In summary, the given expression (6 x^4)(4 y^2) / [ (3 x^2)(16 y) ] simplifies to (1/2) * x^2 * y.