Working with Exponents and Radicals

Exponents and radicals extend our ability to work with numbers, making complex calculations easier.

Properties of Exponents

• \(a^m \cdot a^n = a^{m+n}\)
• \((a^m)^n = a^{mn}\)
• \(a^0 = 1\) (for \(a eq 0\))

Properties of Radicals

• \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)
• \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) (for \(b eq 0\))

Real-World Applications

• Used in scientific notation for big numbers
• Calculating distances in geometry (Pythagorean theorem)

Simplifying Expressions

Knowing these properties helps simplify and solve equations more efficiently.