Problem Solving

If x > 1 and √x ÷ x^3 = x^m, what is the value of m?
(A) -7/2
(B) -3
(C) -5/2
(D) -2
(E) -3/2

x^(1/2) / x^3 = x^m

x^(-5/2) = x^m

[spoiler]m = -5/2[/spoiler]

papgust wrote:x^(1/2) / x^3 = x^m

x^(-5/2) = x^m

[spoiler]m = -5/2[/spoiler]

Perfect solution, here's a little elaboration.

We can write roots as fractional exponents. Hence "root(x)" is the same as "x^(1/2)". Similarly "cuberoot(x)" is the same as "x^(1/3)".

When we divide a power by another power with the same base, we subtract the exponents. so:

x^(1/2) / x^3 = x^(1/2 - 3) = x^(-5/2)

x^(1/2) / x^3 = x^m

Squaring both sides:

x/ x^6 = x^2m

x^(1-6) =x^2m

x^-5 = x^2m

this implies 2m= -5

m=-5/2

got it?