Exponents & Scientific Notation

What you’ll learn

• With the same base, multiply by adding exponents and divide by subtracting; raise a power to a power by multiplying exponents.
• $a^0 = 1$ for $a \neq 0$; $a^{-n} = 1/a^n$ moves factors to the denominator without making the value negative.
• Scientific notation $a \times 10^n$ uses $1 \le a < 10$; positive $n$ for large magnitudes, negative $n$ for small decimals.
• Compare numbers by lining up exponents on $10$, then compare coefficients when the exponent matches.
• Multiply or divide in scientific notation by handling coefficients and exponents separately, then renormalize $a$ if needed.