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

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $x ^ { 1 / 8 } \cdot x ^ { 7 / 8 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $( 12 b ) ^ { 0 }$

Completely factor the polynomial or state that the polynomial is prime. - $( x + 10 ) ^ { 2 } - 16$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 5 x - 5 } { x } \cdot \frac { 5 x ^ { 2 } } { 9 x - 9 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\left. (- 10 x ^ { 5 } y \right) \left( - 2 x ^ { 4 } y ^ { 2 } \right)$

Determine whether the expression is a monomial. If it is a monomial, state the coefficient and degree. - $\frac { 11 } { x }$

Determine whether the expression is a monomial. If it is a monomial, state the coefficient and degree. - $17 x ^ { 7 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $9 \sqrt { 7 } - 3 \sqrt { 7 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\frac { 36 x ^ { 4 } y ^ { 8 } } { 9 x ^ { 3 } y ^ { - 6 } }$

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. -

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } - x - 56$

Completely factor the polynomial or state that the polynomial is prime. - $2 x ^ { 2 } - 12 x + 16$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 5 x } { 0 x + 5 } \cdot \frac { 4 x + 2 } { 3 }$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( x + 4 ) ^ { 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $8 - 125 x ^ { 3 }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } + 20 x + 100$

Completely factor the polynomial or state that the polynomial is prime. - $6 x ^ { 3 } + 17 x ^ { 2 } + 12 x$

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. -

Evaluate. - $( - 4 ) ^ { 3 }$

List all the elements of B that belong to the given set. - $B = \left\{ 14 , \sqrt { 5 } , - 7,0 , \frac { 1 } { 2 } , - 2,2.4,5 \pi , 0.516516516 \ldots \right\}$ Natural numbers