Question 182059
Solve for z:
{{{(z+2)^(-2/3) = 3}}} Write the left side as a positive exponent:
{{{1/(z+2)^(2/3) = 3}}} Multiply both sides by {{{z+2)^(2/3)}}}
{{{1 = 3(z+2)^(2/3)}}} Divide both sides by 3.
{{{1/3 = (z+2)^(2/3)}}} Now raise both sides to the {{{3/2}}}power.
{{{(1/3)^(3/2) = ((z+2)^(2/3))^(3/2)}}} Multiply the exponents on the right side.
{{{1/(3)^(3/2) = (z+2)}}} Simplify the left side.
{{{1/3sqrt(3) = z+2}}} Finally, subtract 2 from both sides.
{{{z = (1/3sqrt(3))-2}}} and this can also be written as:
{{{highlight(z = (1-6sqrt(3))/3sqrt(3))}}}