Question

Find the solution for m such that:%7D%20%20%7D%20%20%3D%20%20x%5E%7Bm%7D%3Cbr%3E%3Cbr%3E%0A%20%20" id="TexFormula1" title=" \frac{1}{ \sqrt[3]{ x^{2} } } = x^{m}
 " alt=" \frac{1}{ \sqrt[3]{ x^{2} } } = x^{m}
 " align="absmiddle" class="latex-formula">

Answer 1

Let's raise the exponent three on both sides of the equation.

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

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

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

1 = x^(2+3m)

X^(2+3m) = 1

For this to be true:

2+3m = 0

3m = -2

m = -2/3