Evaluating expressions with exponents (SAT)

Mathematics SAT Reasoning Test Math section Difficulty 2/5

Beginning of the lesson

What Are Exponents?

An exponent tells you how many times to multiply a number (the base) by itself. Understanding exponents is essential for SAT success!

📐 Basic Exponent Notation

In the expression bⁿ:

b = base (the number being multiplied)
n = exponent (how many times to multiply)

bⁿ = b × b × b × ... × b

(n times)

Example: 2⁴ = 2 × 2 × 2 × 2 = 16

🔑 Essential Exponent Rules for SAT

Rule	Formula	Example
Product Rule	a^m · aⁿ = a^m+n	2³ · 2² = 2⁵ = 32
Quotient Rule	a^m ÷ aⁿ = a^m-n	3⁵ ÷ 3² = 3³ = 27
Power Rule	(a^m)ⁿ = a^m·n	(2³)² = 2⁶ = 64
Zero Exponent	a⁰ = 1	5⁰ = 1
Negative Exponent	a^-n = 1/aⁿ	2^-3 = 1/8

📊 Visualizing Exponential Growth

Watch how quickly values grow with exponents! This chart shows powers of 2:

Interactive visualization — available in the full lesson

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Test questions: 162
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