91Ó°ÊÓ

Multiply using FOIL: \((x+2 y)(3 x+5 y)\)

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x-3)\) b. \((x+5)(x-5)\)

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(2 x^{3} y z^{6}\right)(2 x)^{5}$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)^{2}\) b. \((x+5)^{2}\)

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(3 x^{-4} y z^{-7}\right)(3 x)^{-3}$$

Will help you prepare for the material covered in the next section. \text { Simplify: } x(x+2)+3(x+2)

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(\frac{x^{3} y^{4} z^{5}}{x^{-3} y^{-4} z^{-5}}\right)^{-2}$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(\frac{x^{4} y^{5} z^{6}}{x^{-4} y^{-5} z^{-6}}\right)^{-4}$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(2^{-1} x^{-2} y^{-1}\right)^{-2}\left(2 x^{-4} y^{3}\right)^{-2}\left(16 x^{-3} y^{3}\right)^{0}}{\left(2 x^{3} y^{5}\right)^{2}}$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\frac{\left(2^{1} x^{3} y^{-1}\right)^{-2}\left(2 x^{6} y^{4}\right)^{-2}\left(9 x^{3} y^{3}\right)^{0}}{\left(2 x^{4} y^{6}\right)^{2}}$$