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.