Module 1: Exponents & Scientific Notation

Add Exponents

• Multiply powers with the same base

  • Example: x^1\cdot x^2=x^3

Subtract Exponents

• Divide powers with the same base

  • Example: \frac{x^5}{x^2}=x^{5-2}=x^3

Multiply Exponents

• Power of a Power

  • Example: \left(x^2\right)^3=x^6

Zero Exponents

• ALWAYS EQUALS = 1

  • Example:x^0=1

Negative Exponents

• Put under one to make positive

  • Example:x^{-2}=\frac{1}{x^2}

Scientific Notation with Negative Exponents

• Small, less than the number one

• Scientific Notation: Move the decimal to the left to put the number in standard form

  • Example: 0.0063 = 6.3 \times 10^{-3}

Scientific Notation with Positive Exponents

• Bigger, greater than the number one

• Scientific Notation: Move the decimal to the right to put the number in standard form

  • Example: 5.7 × 10² = 570

Multiply/Divide (Scientific Notation)

• Multiply or divide numbers, then use the exponents power of 10 rules.

  • Divide:4.2 × 10³ ÷ 2.1 × 10² = 2.0 × 10^{3-2} = 2.0 × 10¹ = 20

  • Multiply: 3.0\times10^{2}\times2.0\times10^{1}=6.0\times10^{2+1}=6.0\times10^{3}=6000

Add/Subtract (Scientific Notation)

• Put in the same power of 10, then add or subtract (when needed)

  • Add:4.5 \times 10^{3} + 3.2 \times 10^{4} = 4.5 \times 10^{3} + 32.0 \times 10^{3} = 36.5 \times 10^{3} = 3.65 \times 10^{4}

  • Subtract: 3.2\times10^4-5\times10^3=32.0\times10^3-5.0\times10^3=27.0\times10^3=2.70\times10^4