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1. Zero Exponent: a 0 = 1 2. Product Rule: a n ⋅am = an m+ 3. Quotient Rule: an am = an m− 4. Negative Exponent: a n an − = 1 To move a number or a symbol from the numerator to the denominator (or from the denominator to the numerator), you must change the sign of the exponent. 5. Power Rule: ( )am n = am n⋅ 6.
we’ll look at exponents of zero and exponents that are negative integers. One way to approach exponents of zero is to think about a term divided by itself; for instance, 2 2 =1 because anything over itself is one. However, what happens if we simplified 2 2 using the Quotient Rule that was discussed earlier? 2 2 = 2−2= 0
Use zero and negative exponents. Use the properties of exponents. Solve real-life problems involving exponents. Evaluate each expression.
Elementary Algebra Skill Applying the Exponent Rule for Zero Exponents Simplify. 1) n0 2) (3x)0 3) 5y0 4) −8a0 5) (a + b)0 6) a0 + b0 7) 3x0y 8) 10(mn)0 9) (0.005w)0abc 10) (1 2b) 0 11) −( 1 5) 0 12) 2a0 + (2a)0 + 20a 13) (9x)0 − 9x0−(−9x)0 14) (m + 2)0 − m0 − 2m0 15) (t + v)0t0 + v0 16) 4m(n − 5p)0 5m0 17) (ab 2
the exponents. The second law says that if the expressions are being . divided, you can simplify by . subtracting. the bottom exponent from the top.. These laws show how you can distribute (or un-distribute if . you reverse them) a common exponent to different bases. The first law shows how distributing an exponent works with
1. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents. Examples: A. B. C. 2. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents. Examples: A. B. ˘ C. ˇ ˇ 3. ZERO EXPONENT RULE: Any base (except 0) raised to the zero power is equal to one. ˆ ˙
When an exponent is zero, the value of the power is 1. When an exponent is negative take the reciprocal of the base and make the exponent positive. When multiplying exponents with the same base, keep the base and add the exponents. When dividing exponents with the same base, keep the base and subtract the exponents.
