To simplify the expression, we use the power of a power rule, which states that (a^m)^n = a^(m*n).
In this case, we have (y^9)^5 * y^-6.
By applying the power of a power rule, we multiply the exponents: 9 * 5 = 45.
Therefore, the expression simplifies to y^45 * y^-6.
To combine the terms with the same base, we use the product of powers rule, which states that a^m * a^n = a^(m + n).
In this case, we have y^45 * y^-6.
By applying the product of powers rule, we add the exponents: 45 + (-6) = 39.
Therefore, the final simplified expression is y^39.