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

Write the given set in interval notation and graph the set on a number line. - $\{ x \mid x \leq - 9 \}$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 6 x ^ { 2 } + 12 x - 8 \right) + ( 24 x + 8 )$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $4 ^ { 2 } \cdot 4 ^ { 9 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\left( \frac { 12 x ^ { - 4 } y ^ { - 3 } z ^ { 3 } } { 3 x y ^ { - 3 } z ^ { - 3 } } \right) ^ { - 2 }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( 9 x ^ { 16 } y ^ { - 18 } \right) ^ { 5 / 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } - 16$

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Factor the polynomial by grouping. - $24 x ^ { 2 } + 30 x - 20 x - 25$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } + 9 x - 22$

Simplify the algebraic expression. - $- 4 x - 4 y - 2 x - 8 y$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 54 }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 5 / 3 } \cdot x ^ { - 5 / 6 } } { x ^ { - 1 / 2 } }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\left( x ^ { 8 } \right) ^ { - 6 }$

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

Use the associative property of addition to write an equivalent algebraic expression. - $9 + ( 2 + x )$

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $11 x ^ { 2 } ( - 10 x + 11 )$

Completely factor the polynomial or state that the polynomial is prime. - $32 x ^ { 2 } + 104 x + 60$

Find the intersection of the given intervals. - $( ( \infty , - 6 ) \cup ( - 6 , \infty ) ) \cap ( \infty , 13 ]$

Completely factor the polynomial or state that the polynomial is prime. - $512 - x ^ { 3 }$

Find the quotient and the remainder. - $x ^ { 4 } + 3 x ^ { 2 } + 4$ divided by $x ^ { 2 } + 1$