Exponent Rules Worksheet with Answers for Easy Practice
Exponents are a fundamental concept in mathematics, and understanding their rules is crucial for simplifying expressions and solving equations. This worksheet provides a comprehensive practice on exponent rules, covering the basics and beyond. Work through these exercises to solidify your grasp of exponent rules and sharpen your math skills.
Exponent Rules Basics
Rule 1: Product of Powers
- Rule: a^m × a^n = a^(m+n)
- Example: 2^3 × 2^4 =?
📝 Note: Remember to add the exponents when multiplying like bases.
Answer: 2^(3+4) = 2^7 = 128
Rule 2: Power of a Power
- Rule: (a^m)^n = a^(m×n)
- Example: (3^2)^3 =?
💡 Note: Multiply the exponents when raising a power to another power.
Answer: 3^(2×3) = 3^6 = 729
Rule 3: Power of a Product
- Rule: (ab)^m = a^m × b^m
- Example: (2 × 3)^4 =?
👍 Note: Apply the exponent to each factor in the product.
Answer: 2^4 × 3^4 = 16 × 81 = 1296
Exponent Rules Exercises
Exercise 1
Simplify the following expressions using exponent rules:
- 2^3 × 2^2 =?
- (4^2)^3 =?
- (5 × 2)^4 =?
Answers:
- 2^3 × 2^2 = 2^(3+2) = 2^5 = 32
- (4^2)^3 = 4^(2×3) = 4^6 = 4096
- (5 × 2)^4 = 5^4 × 2^4 = 625 × 16 = 10000
Exercise 2
Evaluate the expressions:
- (3^2 × 3^4) / 3^3 =?
- (2^3)^2 / (2^2)^3 =?
- (5^2 × 5^3) / 5^4 =?
Answers:
- (3^2 × 3^4) / 3^3 = 3^(2+4) / 3^3 = 3^6 / 3^3 = 3^(6-3) = 3^3 = 27
- (2^3)^2 / (2^2)^3 = 2^(3×2) / 2^(2×3) = 2^6 / 2^6 = 1
- (5^2 × 5^3) / 5^4 = 5^(2+3) / 5^4 = 5^5 / 5^4 = 5^(5-4) = 5^1 = 5
Challenge Questions
- Simplify the expression: (2 × 3)^5 / (2^2 × 3^3)
- Evaluate the expression: (5^2)^3 / (5^3)^2
Answers:
- (2 × 3)^5 / (2^2 × 3^3) = (2^5 × 3^5) / (2^2 × 3^3) = 2^(5-2) × 3^(5-3) = 2^3 × 3^2 = 8 × 9 = 72
- (5^2)^3 / (5^3)^2 = 5^(2×3) / 5^(3×2) = 5^6 / 5^6 = 1
Without a solid understanding of exponent rules, solving equations and simplifying expressions can be a daunting task. With this worksheet, you’ve practiced applying these rules to various problems, solidifying your foundation in exponents.
In conclusion, mastering exponent rules takes practice, but with dedication and persistence, you can become proficient in using these rules to simplify expressions and solve equations. Keep practicing, and you’ll soon become an exponent expert!
What is the product of powers rule in exponents?
+The product of powers rule states that a^m × a^n = a^(m+n), where a is the base and m and n are the exponents.
How do you simplify expressions with exponents?
+To simplify expressions with exponents, apply the exponent rules, such as the product of powers rule, power of a power rule, and power of a product rule.
What is the difference between a power of a power and a power of a product?
+A power of a power involves raising a power to another power, whereas a power of a product involves raising a product to a power.
