Radicals allow us to reverse exponent operations. For example, squaring a number such as 5, or (-5) will give us 25. If we take the square root of 25, we get back to 5 or (-5). The same process occurs when we look at higher level roots. A cube root will undo cubing a number. A fourth root will undo raising a number to the fourth power.

Test Objectives
• Demonstrate a general understanding of radicals
• Demonstrate the ability to evaluate radical expressions
• Demonstrate the ability to work with fractional exponents

#1:

Instructions: Simplify each.

a) $$\sqrt[8]{1}$$

b) $$\sqrt[7]{-128}$$

c) $$\sqrt[4]{-16}$$

d) $$-\sqrt{225}$$

e) $$\sqrt[5]{-243}$$

#2:

Instructions: Simplify each.

a) $$\sqrt{14^2}$$

b) $$\sqrt{(-19)^2}$$

c) $$-\sqrt[4]{(-13)^4}$$

d) $$\sqrt[3]{(-5)^3}$$

e) $$\sqrt[6]{(-243)^6}$$

#3:

Instructions: Simplify each.

a) $$(-27)^\frac{1}{3}$$

b) $$(-81)^\frac{1}{2}$$

c) $$-(225)^\frac{1}{2}$$

d) $$(625)^\frac{1}{4}$$

e) $$(-64)^\frac{1}{3}$$

#4:

Instructions: Simplify each.

a) $$\frac{x^{-1}z^2}{z^{-1}(x^{\frac{1}{2}}y^0z^{\frac{3}{2}})^{-2}}$$

#5:

Instructions: Simplify each.

a) $$\frac{(x^{-\frac{5}{3}}x^{-\frac{1}{2}})^{\frac{2}{3}}}{x^{-\frac{5}{3}}}$$

Written Solutions:

#1:

Solutions:

a) $$1$$

b) $$-2$$

c) $$not \hspace{.5em} real$$

d) $$-15$$

e) $$-3$$

#2:

Solutions:

a) $$14$$

b) $$19$$

c) $$-13$$

d) $$-5$$

e) $$243$$

#3:

Solutions:

a) $$-3$$

b) $$not \hspace{.5em} real$$

c) $$-15$$

d) $$5$$

e) $$-4$$

#4:

Solutions:

a) $$z^6$$

#5:

Solutions:

a) $$x^{\frac{2}{9}}$$