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# PROPERTIES OF EXPONENTS

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### PROPERTIES OF EXPONENTS - Page Text Content

FC: Properties of Exponents By. Francesca

1: Positive Power of a Quotient property Words: A quotient raised to a positive power equals the quotient of each base raised to that power. Numbers: (3/5)^4=3/5*3/5*3/5*3/5=3*3*3*3/5*5*5*5=3^4/5^4 EXAMPLE #2: 1/2)^2=1/2*1/2=1*1/2*2=1^2/2^2 EXAMPLE #3: (2/5)^3=2/5*2/5*2/5=2*2*2/5*5*5=2^3/5^3 EXAMPLE #4: (4/5)^1=4/5=4^1/5^1 EXAMPLE #5: (2/3)^4=2/3*2/3*2/3*2/3=2^4/3^4 Algebra: If A and B are nonzero real numbers and n is a positive integer, then (a/b)^n=a^n/b^n

2: Quotient of Powers property Words: The quotient of the two nonzero powers with the same base equals the base raised to the difference of the exponents. Numbers: 6^7/6^4=6^7-^4=6^3 EXAMPLE #2: 1^8/1^4=1^8-^4=1^4 EXAMPLE #3: 2^5/2^4=2^5-^4=2^1 EXAMPLE #4: 3^4/3^3=3^4-^3=4^1 EXAMPLE #5: 4^5/4^3=4^5-^3=4^2 Algebra: If a is a nonzero real number and m and n are integers, then a^m/a^n=a^m-^n

3: Negative Power of a quotient property Words: A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power. Numbers: (2/3)^-4=(3/2)^4=3^4/2^4 EXAMPLE #2: (2/3)^-2=(3/2)^2=3^2/2^2 EXAMPLE #3: (1/3)^-6=(3/1)^6=3^6/1^6 EXAMPLE #4: (4/3)^-8=(3/4)^8=3^8/4^8 EXAMPLE #5: (6/12)^-2=(12/6)^2=12^2/6^2 Algebra: If a and b are nonzero real numbers and n is a positive integer, then (a/b)^-n=(b/a)^n=b^n/a^n

4: Product of Powers property Words: The product of two powers with the same base equals that base raised to the sum of the exponents. Numbers: 6^7*6^4=6^7+^4=6^11 EXAMPLE #2: 1^1*1^7=1^1+^7=1^8 EXAMPLE #3: 2^2*2^2=2^2+^2=2^4 EXAMPLE #4: 3^4*3^5=3^4+^5=3^9 EXAMPLE #5: 4^2*4^3=4^2+^3=4^5 Algebra: If a is any nonzero real number and m and n are integers, then a^m*a^n=a^m+^n

5: Power of a Power Property Words: A power raised to another power equals that base raised to the product of the exponents. Numbers: (6^7)^4=6^7*^4=6^28 EXAMPLE #2: (1^2)^2=1^2*^2=1^4 EXAMPLE #3: (2^4)^4=2^4*^4=2^16 EXAMPLE #4: (3^6)^6=3^6*^6=3^36 EXAMPLE #5: (4^10)^3=4^10*^3=4^30 Algebra: If a is any nonzero real number and m and n are integers, then (a^m)^n=a^mn

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