0. Review of Algebra

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛(8/x⁴)

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers.

$\frac{(\text{∛}mn\cdot \text{∛}{m}^2)}{\text{∛}{n}^2}$

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. $\frac{-4}{\sqrt[3]{3}} + \frac{1}{\sqrt[3]{24}} - \frac{2}{\sqrt[3]{81}}$

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers.

$\frac{5}{\text{∛}2}-\frac{2}{\text{∛}16}+\frac{1}{\text{∛}54}$

Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 1/(2 + √5)

Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. $\frac{\sqrt{7} - 1}{2\sqrt{7} + 4\sqrt{2}}$

Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (p - 4) / (√p + 2)

Rationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. $\frac{3m}{2 + \sqrt{m + n}}$

Concept Check: By what number should the numerator and denominator of $\frac{1}{\text{∛}3-\text{∛}5}$ be multiplied in order to rationalize the denominator? Write this fraction with a rationalized denominator.

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. -3x^-1/3

Write each root using exponents and evaluate. ∜81

If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. -12x^1/2

Find each root. √(-12)²

Solve: $\sqrt{x} + \sqrt{x + 5} = 5$

Solve: 2x^2/3 - 5x^1/3 -3 = 0.