Exam 1: Review of Basic Concepts

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 ^ { - 5 } } { 3 ^ { - 3 } }$

Find the sum or difference. - $\left( 3 + 7 x ^ { 2 } + 9 x ^ { 4 } + 3 x ^ { 3 } \right) + \left( - 7 x ^ { 3 } - 9 x ^ { 2 } + 6 + 3 x ^ { 4 } \right)$

Find the sum or difference. - $( - 9 a + 5 b ) ( - 8 a + 3 b )$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d miles. Use a calculator to determine the duration of a storm with a diameter of 10 miles. Round to the nearest hundredth.

Evaluate the expression. - $64 ^ { 1 / 3 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( - 4 x ^ { 6 } y \right) \left( - 7 x ^ { 4 } y ^ { 5 } \right)$

Factor by any method. - $15 x ^ { 4 } + 22 x ^ { 2 } + 8$

Factor out the greatest common factor. Simplify the factors, if possible. - $20 \mathrm { x } ^ { 10 } + 16 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 5 } + 15 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 5 } + 12 \mathrm { y } ^ { 10 }$

Tell whether the statement is true or false. - $\{ 0,8,11,16 \} = \{ 11,8,16,0 \}$

Find the sum or difference. - $\left( 4 x ^ { 2 } + 3 x - 1 \right) \left( x ^ { 2 } - 3 x - 3 \right)$

Evaluate the expression. - $| 23 |$

Factor, using the given factor. Assume all variables represent positive real numbers. - $( 2 m + 6 ) ^ { - 6 / 5 } + ( 2 m + 6 ) ^ { 1 / 5 } + ( 2 m + 6 ) ^ { 7 / 5 } ; \quad ( 2 m + 6 ) ^ { - 6 / 5 }$

Tell whether the statement is true or false. - $\{ 10,13,14,16 \} \cap \{ 13,14,17,18 \} = \{ 13,14 \}$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 3,4,5,6,7,8,9,10,11,12,13 \} , \mathrm { M } = \{ 3,5,7,9 \} , \mathrm { N } = \{ 4,6,8,10,12 \} , \mathrm { Q } = \{ 3,5,7,9,11,13 \}$ , and $R = \{ 3,4,5,6 \}$ . $\varnothing \cup N$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -The formula $C = \frac { 5 } { 9 } ( F - 32 )$ expresses the relationship between Fahrenheit temperature, $F$ , and Celsius temperature, C. Use the formula to convert $86 ^ { \circ } \mathrm { F }$ to its equivalent temperature on the Celsius scale.

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. -

Simplify the expression. Assume all variables represent positive real numbers. - $4 \sqrt [ 7 ] { x ^ { 8 } y } - 3 x \sqrt [ 7 ] { x y }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x ^ { 2 } y < 0$

Find the sum or difference. - $\frac { 9 y ^ { 4 } + 15 y ^ { 3 } + 5 y - 1 } { 3 y ^ { 2 } + 1 }$

Factor by any method. - $81 x ^ { 2 } - 4$