Exponents & Radicals worksheet - Free Printable

1. Write each of the following in radical form:
a. \(3^{\frac{1}{2}} = \sqrt{3}\)
b. \((-3)^{\frac{2}{3}} = \sqrt[3]{(-3)^2} = \sqrt[3]{9}\)
c. \(-(5)^{\frac{5}{3}} = -\sqrt[3]{5^5} = -\sqrt[3]{3125}\)

2. Write each of the following in exponential form:
a. \(\sqrt{15} = 15^{\frac{1}{2}}\)
b. \(\sqrt[5]{2} = 2^{\frac{1}{5}}\)
c. \(\sqrt[4]{6^3} = 6^{\frac{3}{4}}\)

3. Write as a single positive power and then evaluate:
a. \((-2)^3 \times (-2)^4 = (-2)^{3+4} = (-2)^7 = -128\)
b. \(3^8 \div 3^4 = 3^{8-4} = 3^4 = 81\)
c. \((2^3)^2 = 2^{3 \times 2} = 2^6 = 64\)
d. \((-2)^5 \div (-2)^3 - (-2)^2 = (-2)^{5-3} - (-2)^2 = (-2)^2 - 4 = 4 - 4 = 0\)
e. \(\frac{(3^2)^2 \times 3^{-2}}{2 + 2^0} = \frac{3^{4} \times 3^{-2}}{2 + 1} = \frac{3^{4-2}}{3} = \frac{3^2}{3} = \frac{9}{3} = 3\)