To solve this equation, we need to simplify both sides and find the values of k that satisfy the equation.
Starting with the left side:
x^4/y^(2/3) / y^k / yx^3
= x^4/y^(2/3) * y^(k-1) * x^(-3)
= x^(4-3) * y^(-2/3 + k - 1)
= x * y^(k - 2/3 - 3)
Now, comparing it to the right side (x^3 * y^-4), we have:
x * y^(k - 2/3 - 3) = x^3 * y^-4
Comparing the coefficients, we have:
k - 2/3 - 3 = -4
Simplifying the equation:
k - 2/3 = -1
k = -1 + 2/3
k = -1 + 2/3
k = -1/3
Therefore, the value of k that satisfies the equation is k = -1/3.
if x^4/y^2/3 /y^k/yx^3=x^3y^-4
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