Question

−1^x^2=2^x

Answer 1

I take it you need to solve for x? and ^ means an exponent function, right?

If that assumption is correct, then I'd take the natural log of each side, then use the power rule to change the equation to:
x^2 ln(-1) = xln(2)

From there, you could divide both sides by x, then divide both sides by ln(-1) to solve for x.