Can someone help me understand how to rearrange this equation to get the following answer(s)

(x^p_y^p)^((1/p)-1) * x^(p-1) - Lambda*price1 = 0

(x^p_y^p)^((1/p)-1) * y^(p-1) - Lambda*price2 = 0

p*x + p*x = y = 0

which are my Lagrange multipliers for the cobb douglas function (x^p+y^p)^(1/p) where p is alpha/beta

the answer is

x=y(price1/price2)^(1/(p-1)

lambda = price1x + price2y

My basic math is not up the scratch so could somebody help me understand how to solve for x in the equations given

thanks