Exponent Rules Practice Worksheet
Exponent rules are a fundamental concept in mathematics, and mastering them is essential for solving various math problems. In this practice worksheet, we will provide you with exercises to help you practice and reinforce your understanding of exponent rules.
Product of Powers Rule
The product of powers rule states that when you multiply two numbers with the same base, you add their exponents. Mathematically, this can be represented as:
a^m × a^n = a^(m+n)
Exercise 1:
Simplify the following expressions using the product of powers rule:
- 2^3 × 2^4 =
- 5^2 × 5^6 =
- 3^2 × 3^5 =
Solutions:
- 2^3 × 2^4 = 2^(3+4) = 2^7
- 5^2 × 5^6 = 5^(2+6) = 5^8
- 3^2 × 3^5 = 3^(2+5) = 3^7
📝 Note: Remember to add the exponents when multiplying numbers with the same base.
Power of a Power Rule
The power of a power rule states that when you raise a number with an exponent to another power, you multiply the exponents. Mathematically, this can be represented as:
(a^m)^n = a^(m×n)
Exercise 2:
Simplify the following expressions using the power of a power rule:
- (2^3)^4 =
- (5^2)^6 =
- (3^2)^5 =
Solutions:
- (2^3)^4 = 2^(3×4) = 2^12
- (5^2)^6 = 5^(2×6) = 5^12
- (3^2)^5 = 3^(2×5) = 3^10
💡 Note: Remember to multiply the exponents when raising a number with an exponent to another power.
Power of a Product Rule
The power of a product rule states that when you raise a product to a power, you raise each factor to that power. Mathematically, this can be represented as:
(ab)^m = a^m × b^m
Exercise 3:
Simplify the following expressions using the power of a product rule:
- (2×3)^4 =
- (5×2)^6 =
- (3×4)^5 =
Solutions:
- (2×3)^4 = 2^4 × 3^4
- (5×2)^6 = 5^6 × 2^6
- (3×4)^5 = 3^5 × 4^5
📝 Note: Remember to raise each factor to the power when raising a product to a power.
Quotient of Powers Rule
The quotient of powers rule states that when you divide two numbers with the same base, you subtract their exponents. Mathematically, this can be represented as:
a^m ÷ a^n = a^(m-n)
Exercise 4:
Simplify the following expressions using the quotient of powers rule:
- 2^8 ÷ 2^3 =
- 5^12 ÷ 5^6 =
- 3^10 ÷ 3^5 =
Solutions:
- 2^8 ÷ 2^3 = 2^(8-3) = 2^5
- 5^12 ÷ 5^6 = 5^(12-6) = 5^6
- 3^10 ÷ 3^5 = 3^(10-5) = 3^5
📝 Note: Remember to subtract the exponents when dividing numbers with the same base.
Conclusion
Exponent rules are an essential part of mathematics, and mastering them can help you solve a wide range of math problems. By practicing the exercises provided in this worksheet, you can reinforce your understanding of exponent rules and become more confident in your math skills.
What is the product of powers rule?
+The product of powers rule states that when you multiply two numbers with the same base, you add their exponents.
What is the power of a power rule?
+The power of a power rule states that when you raise a number with an exponent to another power, you multiply the exponents.
What is the power of a product rule?
+The power of a product rule states that when you raise a product to a power, you raise each factor to that power.
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