9y^−3 ⋅ 2y^11

When multiplying two terms with the same base (y in this case), you add the exponents.

So, 9y^-3 * 2y^11 = 9 * 2 * y^(-3 + 11) = 18y^8

Therefore, the simplified expression is 18y^8.

7y^7 ⋅ 6y^−4

To multiply two terms with the same base (y in this case), you add the exponents.

So, 7y^7 * 6y^-4 = 7 * 6 * y^(7 + (-4)) = 42y^3

Therefore, the simplified expression is 42y^3.

9y^3 ⋅ (?)=−36y^6

To solve for the missing term when 9y^3 is multiplied by it resulting in -36y^6, we can set up the equation:

9y^3 * x = -36y^6

We can simplify the equation by dividing by 9y^3 on both sides:

x = -36y^6 / 9y^3

Simplify the right side by dividing the coefficients and subtracting the exponents of y:

x = -4y^(6-3)
x = -4y^3

Therefore, the missing term is -4y^3.

7y^7 ⋅ 3y^10

To multiply two terms with the same base (y in this case), you simply add the exponents.

7y^7 * 3y^10 = 7 * 3 * y^(7 + 10) = 21y^17

Therefore, the simplified expression is 21y^17.