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Understanding and Applying Exponent Rules
May 11, 2025
Exponent Rules Summary and Application
Overview
Review of exponent rules.
Application of all four rules together in examples.
Importance of understanding each rule for effective problem-solving.
Exponent Rules
Rule 1: Multiplying with Same Base
Example:
(2^3 \times 2^5)
Rule:
When bases are the same,
add
exponents.
Result:
(2^{3+5} = 2^8)
Rule 2: Dividing with Same Base
Example:
(3^8 \div 3^2)
Rule:
When bases are the same,
subtract
exponents.
Result:
(3^{8-2} = 3^6)
Rule 3: Power of a Power
Example:
((3^2)^3)
Rule:
Multiply the exponents.
Result:
(3^{2\times3} = 3^6)
Rule 4: Zero Exponent
Rule:
Anything raised to the power of zero equals 1.
Example:
(a^0 = 1)
Applying Exponent Rules
Example 1
Expression:
(2^8 \div 2^3)
Process:
Division (Rule 2) (\rightarrow 2^{8-3} = 2^5)
Example 2
Expression:
(2^8 \times 2)
Process:
Multiplication (Rule 1) (\rightarrow 2^{8+1} = 2^9)
Example 3
Complex Expression:
((3^4 \times 3^2) \div 3^5)
Process:
Inside Bracket: Rule 1 (\rightarrow 3^{4+2} = 3^6)
Apply Rule 2: (3^6 \div 3^5 = 3^{6-5} = 3^1)
Final: Apply Rule 3 on remaining expression
Example 4
Expression:
(3^{4\times3} \times (3^2 \div 3^5))
Process:
Simplify using Rule 2 and Rule 1
Result: (3^7)
Example 5
Expression:
(3^0 \times 4)
Process:
Apply Rule 4: (3^0 = 1)
Simplifies to: (1 \times 4 = 4)
Example 6
Expression:
((2^6 \times 2^3 \times 2^4) \div (2^5)^2)
Process:
Use Rule 1 for numerator (2^{6+3+4} = 2^{13})
Apply Rule 3 to denominator ((2^5)^2 = 2^{10})
Final: Use Rule 2 (2^{13-10} = 2^3)
Conclusion
Always keep the base the same across operations.
Use rules systematically to simplify expressions.
Practice with examples to strengthen understanding and application of exponent rules.
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