Question

Find the value of ( y^3/2y^-1/2 = 1/3/1/4y + 1 ).

a) ( 1/2 )
b) ( 1/3 )
c) ( 1/4 )
d) ( 1/5 )

Answer 1

To find the value of the expression, simplify both sides of the equation and solve for y.

Step-by-step explanation:

To find the value of the expression, we need to simplify it.

We can simplify ( y^(3/2)y^(-1/2) ) as y^((3/2) - (1/2)) = y^(2/2) = y. Next, we simplify (1/3) / (1/4y + 1) as (1/3) * (1 / (1/4y + 1)).

Multiplying both numerator and denominator by the reciprocal of (1/4y + 1), we get (1/3) * (4y + 1) / 1 = (4y + 1) / 3.

So, we have y = (4y + 1) / 3. To solve for y, we can cross-multiply, giving us 3y = 4y + 1. Then, we can subtract 4y from both sides, which gives -y = 1.

Finally, dividing both sides by -1, we find that y = -1.