Question 188129
If the equation is simply {{{y-2=-4}}}, then...


{{{y-2=-4}}} Start with the given equation



{{{y=-4+2}}} Add 2 to both sides



{{{y=-2}}} Combine like terms.



The solution is {{{y=-2}}} (if the equation is {{{y-2=-4}}})





OR....



Note: Use the caret symbol ^ to signify an exponent


Ex: x squared = x^2

Ex: y to the negative 2nd power = y^(-2)





If the problem is really {{{y^(-2)=-4}}} (since you posted the problem to the exponents section), then....



{{{y^(-2)=-4}}} Start with the given equation



{{{1/y^2=-4}}} Rewrite {{{y^(-2)}}} as {{{1/y^2}}}



{{{1=-4y^2}}} Multiply both sides by {{{y^2}}}



{{{1/(-4)=y^2}}} Divide both sides by {{{-4}}}



{{{-1/4=y^2}}} Reduce



{{{y^2=-1/4}}} Rearrange the equation



{{{y=sqrt(-1/4)}}} or {{{y=-sqrt(-1/4)}}}  Take the square root of both sides



{{{y=(1/2)i}}} or {{{y=-(1/2)i}}} Simplify 



So the solutions are {{{y=(1/2)i}}} or {{{y=-(1/2)i}}} (if the equation is {{{y^(-2)=-4}}})