Laws of Exponents
What are laws of exponents?
exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent
What are the 7 rules of exponents?
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RULE 1: Zero Property.
RULE 2: Negative Property.
RULE 3: Product Property.
RULE 4: Quotient Property.
RULE 5: Power of a Power Property.
RULE 6: Power of a Product Property.
RULE 7: Power of a Quotient Property.
8 laws of exponents
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Zero Exponent Law: a0 = 1.
Identity Exponent Law: a1 = a.
Product Law: am × an = a. m+n
Quotient Law: am/an = a. m-n
Negative Exponents Law: a-m = 1/a. m
Power of a Power: (am)n = a. mn
Power of a Product: (ab)m = amb. m
Power of a Quotient: (a/b)m = am/b. m
Examples
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Example 1: What is the simplification of 55 × 51 ?Solution: 55 × 51 = 55+1 = 56
Example 2: What is the simplification of (−6)-4 × (−6)-7?Solution: (−6)-4 × (−6)-7 = (-6)-4-7 = (-6)-11
Formula
The important laws of exponents are given below: am×an = a. am/an = a. (am)n = a