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√x ÷ x^3 = x^m

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by sanju09 » Thu Jul 08, 2010 12:55 am
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
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by papgust » Thu Jul 08, 2010 1:06 am
x^(1/2) / x^3 = x^m

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

[spoiler]m = -5/2[/spoiler]
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by Stuart@KaplanGMAT » Thu Jul 08, 2010 10:45 am
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)
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by ankurmit » Thu Jul 08, 2010 8:25 pm
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

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