If the expression (6x ^ (5/4) * y ^ (- 5/4))/(root(4, 81x ^ 2 * y)) is written in the form a * x ^ b * y ^ c , then what is the product of a , b and c?

Question

can you please explain each step

Answer 1

The root(4, quantity) part can be expressed as ( quantity )^1/4 so you have:

6x^5/4y^-5/4 / (81x²y)^1/4

Taking the 4th root of denominator (recall (w^h)^k = w^hk where k = 1/4 in this case):

= 6x^5/4y^-5/4 / (3x^2/4y^1/4)

Now apply w^h/w^k = w^(h-k) to simplify:

= 2x^3/4y^-6/4

= 2x^3/4y^-3/2 <<<< this is the form a•x^b•y^c

a=2

b=3/4

c=-3/2

abc = -9/4