91Ó°ÊÓ

For which values of \(a\) and \(b\) is it true that \((a b)^{-1}=\) \(a^{-1} b^{-17}\) Find a pair of nonzero values for \(a\) and \(b\) for which \((a+b)^{-1} \neq a^{-1}+b^{-1}\)

Perform the indicated operations. A variable used in an exponent represents an integer; a variable used as a base represents a nonzero real number. \(z^{3 w}-z^{2 w}\left(z^{1-w}-4 z^{w}\right)\)

Factor each polynomial completely. $$-7 a^{2} b^{2}+7$$

Use a calculator to help you perform the following operations. $$(3.2 x-4.5)(5.1 x+3.9)$$

Perform the indicated operations. A variable used in an exponent represents an integer; a variable used as a base represents a nonzero real number. \(\left(w^{p}-1\right)\left(w^{2 p}+w^{p}+1\right)\)

Laying tile. Lorinda is planning to redo the floor in her bedroom, which has an area of 192 square feet. If the width of the rectangular room is 4 feet less than the length, then what are its dimensions?

Factor each polynomial completely. $$7 x-7 h-h x+h^{2}$$

Perform the indicated operations. A variable used in an exponent represents an integer; a variable used as a base represents a nonzero real number. \(\left(x^{2 r}+y\right)\left(x^{4 r}-x^{2 r} y+y^{2}\right)\)

Which of the following expressions has a value different from the others? Explain. a) \(-1^{-1}\) b) \(-3^{0}\) c) \(-2^{-1}-2^{-1}\) d) \((-1)^{-2}\) e) \((-1)^{-3}\)

Factor each polynomial completely. $$ 6 m^{3}-m^{2} n-2 m n^{2} $$