How do i solve root3{(ab^2c)/(64bc^2)} * root4{(16a^4)/(bc) ?

root3{(ab^2c)/(64bc^2)} * root4{(16a^4)/(bc)

1 Answer
Jun 8, 2018

(root(3)(a.b.c).a)/(2root(4)(b.c))

Explanation:

We use exponential law:

a^2 xx a^4 = a^(2+4) = a^6

a^2/a^3 = a^(2-3) = a^-1

1/a = a^-1

sqrta = a^(1/2)

root(3)a = a^(1/3)

so we have:

root(3)((ab^2c)/(64bc^2)) . root(4)((16a^4)/(bc))

Step 1:

root(3)((ab^2c)/(64bc^2)) = (a^(1/3)b^(2/3)c)/(64^(1/3)b^(1/3)c^(2/3))

(a^(1/3)b^(2/3)c)/(64^(1/3)b^(1/3)c^(2/3)) = ((a^(1/3).b^(2/3 - 1/3).c^(1-2/3))/4) = color(red)((a^(1/3). b^(1/3).c^(1/3))/4)

Step 2:

root(4)((16a^4)/(bc)) = (16^(1/4).a^(4/4))/(b^(1/4).c^(1/4) = color(red)((2.a)/(b^(1/4).c^(1/4))

Step 3: Multiply and simplify the variables in color RED.

color(red)((a^(1/3). b^(1/3).c^(1/3))/4) . color(red)((2.a)/(b^(1/4).c^(1/4)) = (root(3)(a.b.c).a)/(2root(4)(b.c))