91Ó°ÊÓ

The factors in the following exercises involve fractions or decimals. Apply the methods of this section, and find each product. $$ (0.3 x-1.6 y)^{2} $$

Apply the quotient rule for exponents, if possible, and write each result using only positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{5^{-4}}{5^{2}} $$

The tables give some selected ordered pairs for functions \(f\) and \(g\). $$ \begin{array}{c|c|c|c|c} x & 3 & 4 & 6 & 8 \\ \hline f(x) & 1 & 3 & 9 & 2 \end{array} $$ $$ \begin{array}{c|c|c|c|c} x & 2 & 7 & 1 & 9 \\ \hline g(x) & 3 & 6 & 9 & 12 \end{array} $$ Tables like these can be used to evaluate composite functions. For example, to evaluate \((g \circ f)(6),\) use the first table to find \(f(6)=9 .\) Then use the second table to find $$ (g \circ f)(6)=g(f(6))=g(9)=12 $$ Find each of the following. \((f \circ g)(7)\)

Apply the quotient rule for exponents, if possible, and write each result using only positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{y^{5}}{t^{3}} $$

Find each product. $$ [((3 m-y)+z][(3 m-y)-z] $$

The perimeter \(x\) of a square with sides of length \(s\) is given by the formula \(x=4 s\). (a) Solve for \(s\) in terms of \(x\). (b) If \(y\) represents the area of this square, write \(y\) as a function of the perimeter \(x\) (c) Use the composite function of part (b) to find the area of a square with perimeter 6 .

Find each product. $$ (m-5 p)\left(m^{2}-2 m p+3 p^{2}\right) $$

Find each product. $$ (4 z-x)\left(z^{3}-4 z^{2} x+2 z x^{2}-x^{3}\right) $$

For each pair of functions, find \((f g)(x)\). $$ f(x)=x-7, \quad g(x)=4 x+5 $$

Simplify each expression. Assume that all variables represent nonzero real numbers. $$ \left(5^{-3}\right)^{-2} $$