Exam 1: Review of Basic Concepts

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( x ^ { - 3 } \right) ^ { 0 } } { 6 x ^ { - 6 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 49 } { 5 } }$

Factor by any method. - $36 x ^ { 2 } - 25$

Perform the indicated operations. - $\frac { 3 } { 4 x } + \frac { 7 } { 8 x }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 6 } { 7 } } - \sqrt { \frac { 216 } { 252 } }$

Find the product or quotient. - $\frac { 5 p - 5 } { p } \cdot \frac { 8 p ^ { 2 } } { 9 p - 9 }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 5,6,7,8,9,10 \} , \mathrm { B } = \{ 7,9,11 \} , \mathrm { C } = \{ 5,6,8,10 \} , \mathrm { D } = \{ 5,10 \}$ , and $\mathrm { U } = \{ 5,6,7,8,9,10,11 \}$ . $C \subseteq \varnothing$

Evaluate the expression. - $( - 3 ) ^ { 3 }$

Use the distributive property to rewrite a sum as a product or the product as a sum. --11y + 17y

Tell whether the statement is true or false. - $\{ x \mid x \text { is a natural number greater than } 1 \} = \{ 1,2,3 , \ldots \}$

Identify the expression as a polynomial or not a polynomial. - $4 x ^ { 4 } + 5 x ^ { 2 } - 17$

Round to two decimal places unless otherwise indicated. If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the -Suppose the cost per ton, $\mathrm { y }$ , to build an oil platform of $\mathrm { x }$ thousand tons is approximated by $\mathrm { y } =$ $\frac { 112,500 } { x + 225 }$ . What is the cost per ton for $x = 100 ?$

Find the sum or difference. - $\left( 2 n ^ { 7 } - 9 n - 7 n ^ { 6 } \right) + \left( - 4 n ^ { 6 } + 5 n ^ { 7 } - 6 n \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $6 \sqrt { 80 x ^ { 2 } } - 3 \sqrt { 45 x ^ { 2 } } - \sqrt { 5 x ^ { 2 } }$

Solve the equation - $\frac { x ^ { 4 } + 4 x ^ { 2 } + 6 } { x ^ { 2 } + 1 }$

Factor by any method. -Find all values of a that will make the polynomial a perfect square trinomial. $36 x ^ { 2 } + a x + 25$

Factor the trinomial, if possible. - $15 x ^ { 2 } + 26 x + 8$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)$

Find the sum or difference. - $\left( - 8 - 9 x ^ { 2 } + 4 x ^ { 4 } + 2 x ^ { 3 } \right) + \left( 3 x ^ { 3 } - 4 x ^ { 2 } + 6 + 2 x ^ { 4 } \right)$

Factor by grouping. - $6 x ^ { 10 } - 9 x ^ { 5 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } - 12 y ^ { 6 }$