Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $- 8 x ^ { 7 } \left( 6 x ^ { 2 } - 5 \right)$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 18 x + 81 } \cdot \frac { x ^ { 2 } + 17 x + 72 } { x ^ { 2 } + 10 x + 16 }$

Evaluate the algebraic expression for the indicated variable. - $\left| 4 a ^ { 2 } - b ^ { 2 } \right| + c$ for $a = - 9 , b = 1 , c = 19$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $- 32 ^ { 1 / 5 }$

Simplify the rational expression. - $\frac { x ^ { 2 } - 25 } { x - 5 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $- 3 ^ { - 2 }$

Factor the polynomial by grouping. - $3 x ^ { 2 } + 7 x + 21 x + 49$

Sets A, B, and C are given. Find the indicated set. A = {-8, -3, -1, 2, 5}, B = {-3, 2, 5, 7}, and C = {-1, 4, 9} - $B \cup C$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( x ^ { 2 } + 1 \right) - \left( 8 x ^ { 2 } - 4 \right) + \left( x ^ { 2 } + x + 4 \right)$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 3 } { x } + \frac { 7 } { x ^ { 2 } } } { \frac { 9 } { x ^ { 2 } } - \frac { 49 } { x } }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 1 } { x + 6 } \div \frac { 5 } { x ^ { 2 } - 36 }$

Sets A, B, and C are given. Find the indicated set. A = {-8, -3, -1, 2, 5}, B = {-3, 2, 5, 7}, and C = {-1, 4, 9} - $( A \cap B ) \cup C$

Evaluate. - $( 11 x ) ^ { 2 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { 625 }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 4 } + 14 x ^ { 2 } + 49$

Simplify the radical expression. Assume all variables represent positive real numbers. - $- 8 \sqrt { 7 } - 6 \sqrt { 63 }$

List all the elements of B that belong to the given set. - $B = \left\{ 4 , \sqrt { 8 } , - 11,0 , \frac { 0 } { 4 } , 0.7 , - 8 \pi , 0.161616 \ldots \right\}$ Irrational numbers

Factor the polynomial by grouping. - $x ^ { 2 } + 9 x + 2 x + 18$

Completely factor the polynomial or state that the polynomial is prime. - $4 x ^ { 2 } - 14 x - 8$

List all the elements of B that belong to the given set. - $B = \left\{ 15 , \sqrt { 8 } , - 6,0 , \frac { 0 } { 1 } \right\}$ Real numbers