x⁹/x²

To simplify the expression x⁹/x², we can subtract the exponents:

x⁹/x² = x^9-2 = x^7

Therefore, x⁹/x² simplifies to x^7.

h^14/h^5

To simplify the expression h^14/h^5, we can use the quotient rule of exponents:

h^14/h^5 = h^(14-5) = h^9

Therefore, h^14/h^5 simplifies to h^9.

4^4/4^6

To simplify the expression 4^4/4^6, we can use the quotient rule of exponents:

4^4/4^6 = 4^(4-6) = 4^(-2)

Recall that a negative exponent indicates the reciprocal of a power. Therefore:

4^(-2) = 1/4^2 = 1/16

Thus, 4^4/4^6 simplifies to 1/16.

5^0

Any non-zero number raised to the power of zero is 1. Hence,

5^0 = 1.

7^4/7^2 ___ 49

To solve 7^4/7^2, we can use the quotient rule of exponents:

7^4/7^2 = 7^(4-2) = 7^2

So, 7^4 / 7^2 simplifies to 49 (which is 7^2).

We can write 7^4 / 7^2 = 7^2 = 49

-2r(8r+5)

-2r(8r+5) can be simplified by using the distributive property of multiplication over addition:

-2r(8r+5) = -2r * 8r - 2r * 5

= -16r^2 -10r

So, -2r(8r+5) simplifies to -16r^2 -10r.

4a(a^2+7a+4)

Expanding the expression using the distributive property, we get:

4a(a^2+7a+4) = 4a * a^2 + 4a * 7a + 4a * 4

= 4a^3 + 28a^2 + 16a

Therefore, 4a(a^2+7a+4) simplifies to 4a^3 + 28a^2 + 16a.

(2y-3)(3y_2)

To multiply (2y-3)(3y+2), we can use the distributive property:

(2y-3)(3y+2) = 2y * 3y + 2y * 2 - 3 * 3y - 3 * 2

= 6y^2 + 4y - 9y - 6

= 6y^2 - 5y - 6

Therefore, (2y-3)(3y+2) simplifies to 6y^2 - 5y - 6.

(2y-3)(3y-2)

To multiply (2y-3)(3y-2), we can use the distributive property:

(2y-3)(3y-2) = 2y * 3y + 2y * (-2) - 3 * 3y - 3 * (-2)

= 6y^2 - 4y - 9y + 6

= 6y^2 - 13y + 6

Therefore, (2y-3)(3y-2) simplifies to 6y^2 - 13y + 6.