Solve for y (x^y)/(x^3)=x^6

$\frac{x^{y}}{x^{3}} = x^{6}$

Move $x^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{y} x^{- 3} = x^{6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{y - 3} = x^{6}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$y - 3 = 6$

Move all terms not containing $y$ to the right side of the equation.

Add $3$ to both sides of the equation.

$y = 6 + 3$

Add $6$ and $3$ .

$y = 9$