Compute and simplify so that only positive exponents remain.

$$\left(\frac{x^{-2}}{y}\right)^{-3}$$

Suppose that

$$P ( x ) = x ^ { 100 } - x ^ { 99 } + x ^ { 98 } - x ^ { 97 } + \cdots + x ^ { 2 } - x + 1$$

. Find the remainder when P(x) is divided by x + 1.

Simplify the remaining expression completely.

$$\dfrac{x^6y^4}{xy^2}$$

Determine if $P(x)=3 x^3-4 x^2-28 x-16$ has a zero remainder when divided by $x+2$. Determine $Q(x)$.

Find the quotient and the remainder.

$$\frac { 1 - 2 x + 3 x ^ { 2 } - 4 x ^ { 3 } } { x - 2 }$$

Solve the system.

$$2(5 a-5 b)=10$$

$$-5(6 a+2 b)=10$$

Determine the inverse of the linear function, where y=f(x).

$$y-y_1=m\left(x-x_1\right)$$

Find the quotient q(x) and remainder r(x) when ƒ(x) is divided by g(x). ƒ(x) = 2x³ - 3x² + x - 1, g(x) = 3x³ + 4x - 5

Add or subtract.

$$\frac{5}{c-5}+\frac{9}{c-5}$$

Pickled cucumbers remain edible much longer than fresh cucumbers do. Explain.

Find the quotient and the remainder when the first polynomial is divided by the second.

$$2 x^3+x^2+3 x+7 ; x+2$$

Does the quotient of 4554 ÷ 9 have a remainder? How can you tell without dividing?

Simplify. $-5 n\left(2 n^2\right)-(-5 n)(8 n)+(-5 n)(4)$

Verify each identity.

$$\sin t \tan t = \frac { 1 - \cos ^ { 2 } t } { \cos t }$$