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. - $64 ^ { - 4 / 3 }$

Completely factor the polynomial or state that the polynomial is prime. - $36 x ^ { 2 } - 1$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x } { 7 } - \frac { 5 } { 11 }$

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

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 21 x - 21 } { 11 } \div \frac { 7 x - 7 } { 99 }$

Find the quotient and the remainder. - $x ^ { 2 } + 10 x + 16$ divided by $x + 4$

Completely factor the polynomial or state that the polynomial is prime. - $( x - 1 ) ^ { 2 } - 25$

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} - $\mathrm { A } \cup \mathrm { C }$

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

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x - \frac { x } { x + 7 } } { x + 6 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $x ^ { 6 } \cdot x ^ { 5 }$

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

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 11 } } { x ^ { 6 } }$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 6 x ^ { 2 } + 7 x - 8 \right) + \left( 4 x ^ { 2 } + 6 x + 3 \right)$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 5 x - 11 ) ^ { 2 }$

Use the commutative property of addition to write an equivalent algebraic expression. -x + 5

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( x - 5 ) ^ { 2 }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\frac { \left( 3 x ^ { 1 / 3 } \right) ^ { 4 } } { x ^ { - 6 / 5 } }$

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 out the greatest common factor. - $5 x ^ { 2 } - 30 x$