The product of $$1.5\times3^{10}$$  and $$2\times3^2$$  is ________.

$$\left(5xy\right)^2+2x^3$$  has a degree equal to _______.

Simplify $$\left(\frac{1}{2}-\frac{1}{4}\right)^{-1}$$  

Which of the following is equivalent to $$-\left(-2\right)^0-\left(5^0\right)$$ ?

Express the simplified form of $$3x^3+9x-3x^2+10x-2+8x^2$$  in standard form.

Determine the value of $$18x-3\left(2x+y\right)^2$$  when $$x=1$$  and $$y=-1$$ .

Simplify: $$\frac{\left(a^{-2}b^3\right)^{-2}}{\left(a^{-1}b^2\right)\left(a^2b^{-3}\right)}$$  

Evaluate: $$5x^3+2xy-3x^2+10y$$  for $$x=2$$  and $$y=-3$$ .

Express $$5x\left(x^2+2x\right)-5\left(x^2+1\right)$$  in simplest form.

What is the quotient if $$x^2+8x+15$$  is divided by $$x+3$$ ?

Determine the remainder when $$x^5+x^4+x^3+x+1$$  is divided by $$x+1$$ .

What should be the value of $$k$$  so that $$x^3+kx^2+8$$  is equal to the product of $$\left(x+2\right)$$  and $$\left(x^2-2x+4\right)$$ ?

A rope is $$\left(x^3-x^2-2x+8\right)$$  meters long. The rope is to be divided into pieces of equal length. If each piece should be $$\left(x+2\right)$$  meters long, how many pieces can be made?

What would be the area of a rectangle if its width and length are given by $$\left(3x+4\right)$$  and $$\left(5x-1\right)$$ , respectively?