Properties of Exponents Worksheet
Explore the fundamental properties of exponents including product rule, quotient rule, and power rule through various exercises for 6th graders.
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Properties of Exponents
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Read each question carefully and answer by applying the properties of exponents. Show your work where necessary.
1. Which expression is equivalent to 5³ × 5⁴?
5⁷
5¹²
25⁷
25¹²
2. Simplify: (2²)³
2⁵
2⁶
6²
8²
3. According to the product rule, when multiplying exponents with the same base, you the powers. For example, xᵃ * xᵇ = x .
4. The quotient rule states that when dividing exponents with the same base, you the powers. For example, xᵃ / xᵇ = x .
5. The power rule states that when raising a power to another power, you the powers. For example, (xᵃ)ᵇ = x .
6. Explain in your own words why 4² is not the same as 4 × 2.
7. Simplify the expression (x⁵y²)³ using the properties of exponents.
8. Any non-zero number raised to the power of zero is equal to one.
True
False
9. When dividing exponents with the same base, you multiply the powers.
True
False
Match each expression with its simplified form.
10. 3² × 3⁵
a. x⁶
11. (x³)²
b. 3⁷
12. y⁸ / y³
c. y⁵