Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { 1 } { \sqrt { 3 } } + \frac { 5 } { \sqrt { 27 } } - \frac { 3 } { \sqrt { 12 } }$

Find the domain of the expression. - $\frac { x - 8 } { 4 + x }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. -At an altitude of h feet above the surface of the earth, the approximate distance in miles that a person can see is given by $\mathrm { d } = 1.2247 \sqrt { \mathrm { h } }$ How far can a person see if if he or she is 920 feet above the earth's surface? Round Your answer to the nearest tenth of a mile.

Decide whether the expression has been simplified correctly. - $( a b ) ^ { 4 } = a b ^ { 4 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( - 2 t ^ { 5 } \right) \left( 5 t ^ { 2 } \right) \left( - 3 t ^ { 7 } \right)$

Factor, using the given factor. Assume all variables represent positive real numbers. - $6 \mathrm { k } ^ { - 3 } + \mathrm { k } ^ { - 5 } ; \quad \mathrm { k } ^ { - 5 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 2 } } { x ^ { - 4 } }$

Evaluate the expression. - $( - 121 ) ^ { 1 / 2 }$

Evaluate the expression. -Let $x = 6$ and $y = - 3$ . Evaluate $\frac { | x | } { x } + \frac { | y | } { y }$ .

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\left( \frac { 2 } { 5 } \right) ^ { - 2 }$

Determine which property of absolute value justifies the statement. - $| - x | = | x |$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { \frac { 27 x ^ { 3 } } { y 5 } }$

Identify the expression as a polynomial or not a polynomial. - $7 x ^ { 5 } + 4 x ^ { 2 } - 14$

Factor out the greatest common factor. Simplify the factors, if possible. - $10 x ^ { 6 } + 15 x ^ { 3 } - 6 x ^ { 3 } - 9$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 8,9,10,11,12,13 \} , \mathrm { B } = \{ 10,12,14 \} , \mathrm { C } = \{ 8,9,11,13 \} , \mathrm { D } = \{ 8,13 \}$ , and $\mathrm { U } = \{ 8,9,10,11,12,13,14 \}$ . $\mathrm { A } \subseteq \mathrm { B }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 17 x ^ { 2 }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $4 + ( - 4 ) = 0$

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

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\mathrm { z } ^ { - 2 / 5 } \cdot \mathrm { z } ^ { 3 / 5 }$

Tell whether the statement is true or false. - $\{ 1,6,4,7 \} = \{ 4,1,6 \}$