TRACK 1 • NUMBER SENSEStrand: Number Sense and Arithmetic Operations
Exponents and Powers Smart Lab
Learn repeated multiplication, exponent laws, negative powers, standard form, and real-life exponential growth.
What are Exponents?
Exponents are a compact way to write repeated multiplication. In \(a^n\), a is the base and n is the exponent or power.
Example: \(2^5 = 2 × 2 × 2 × 2 × 2 = 32\)
Standard Form: Large or small numbers can be written as \(m × 10^n\), where \(1 ≤ m < 10\).
Example: \(3,600,000 = 3.6 × 10^6\) and \(0.00042 = 4.2 × 10^{-4}\)
2⁵ = 32
Formula Hub
Product Rule
\(a^m × a^n = a^{m+n}\)
Same base: add exponents.
Quotient Rule
\(a^m ÷ a^n = a^{m-n}\)
Same base: subtract exponents.
Power of Power
\((a^m)^n = a^{mn}\)
Multiply the exponents.
Zero Exponent
\(a^0 = 1\), for \(a ≠ 0\)
Negative Exponent
\(a^{-n}=\frac{1}{a^n}\)
Standard Form
\(m × 10^n\), where \(1 ≤ m < 10\)
Guided Solve Lab
Activity Zone
🎛️ Power Builder
Change base and exponent to see repeated multiplication.
🧮 Powers Table
⚔️ Compare Powers
Which is greater?
2⁶
4³
🔬 Standard Form Converter
🧩 Rule Identifier
\(2^3 × 2^4\)
Worksheet Generator
Generate printable practice on exponent laws, evaluating powers, negative exponents, and standard form.
Real-Life Lab
Teacher Tools
Learning Outcomes
- Explain exponents as repeated multiplication.
- Identify base and exponent in \(a^n\).
- Apply product, quotient, power, zero, and negative exponent rules.
- Convert large and small numbers to standard form.
- Connect exponents to growth, storage, biology, finance, and science.
Exit Ticket Prompts
- Why is \(2^5\) not the same as \(2 × 5\)?
- Simplify \(3^4 × 3^2\).
- Write 45,000 in standard form.