Powers and Roots Demystified

Exponents and radicals are essential tools for simplifying expressions and solving equations on the SAT, especially when you can't use a calculator.

Working with Exponents

An exponent tells you how many times to multiply a base by itself. Key rules include:

• Product Rule: \( a^m \times a^n = a^{m+n} \)
• Quotient Rule: \( \frac{a^m}{a^n} = a^{m-n} \)
• Power Rule: \( (a^m)^n = a^{mn} \)

Understanding Radicals

A radical, like \( \sqrt{x} \), asks what number multiplied by itself equals \( x \). Exponents and roots are closely related: \( \sqrt{x} = x^{1/2} \).

Real-World Applications

Exponents are used in science for growth and decay, while radicals appear in geometry, such as finding the side of a square with a given area.