Power Surge Worksheet
POWER SURGE
Basic Exponent Rules • Step-by-Step Practice
Name:
Date: Period:
1. Multiply: Add Powers
\(x^a \cdot x^b = x^{a+b}\)
Example: \(x^2 \cdot x^3 = x^{2+3} = x^5\)
2. Divide: Subtract Powers
\(\frac{x^a}{x^b} = x^{a-b}\)
Example: \(\frac{x^6}{x^2} = x^{6-2} = x^4\)
3. Power to Power: Multiply
\((x^a)^b = x^{a \cdot b}\)
Example: \((x^3)^2 = x^{3 \cdot 2} = x^6\)
1
Part 1: Product of Powers
Action: Keep the base, add exponents
Problem 1 Add exponents
\( x^3 \cdot x^4 \)
Answer:
Problem 2 Add exponents
\( y^5 \cdot y^2 \)
Answer:
Problem 3 Add exponents
\( a^6 \cdot a^3 \)
Answer:
2
Part 2: Quotient of Powers
Action: Keep the base, subtract exponents
Problem 4 Subtract exponents
\( \frac{x^7}{x^3} \)
Answer:
Problem 5 Subtract exponents
\( \frac{y^9}{y^4} \)
Answer:
Problem 6 Subtract exponents
\( \frac{m^8}{m^2} \)
Answer:
3
Part 3: Power of a Power
Action: Keep the base, multiply exponents
Problem 7 Multiply exponents
\( (x^3)^2 \)
Answer:
Problem 8 Multiply exponents
\( (y^4)^3 \)
Answer:
Problem 9 Multiply exponents
\( (m^5)^2 \)
Answer:
Golden Rule to Remember: In all three rules, the base stays the exact same! You only operate on the exponent numbers (add, subtract, or multiply).
