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Laws of Exponents
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Key Concepts:
Terms in this set (32)
Product rule definition
multiplying two powers that have the same base, you can add exponents
Product rule formula
a^n x a^m = a^(n=m)
Product rule example 1
2^3 x 2^4 = 2^(3+4) = 2^7
Product rule example 2
6^2 x 6^9= 6^(2+9) = 6^11
Quotient rule definition
keep the base and subtract the exponents
Quotient rule formula
a^n/a^m = a^(n-m)
Quotient rule example 1
(9x^3)/(3x^1) =3x^2
Quotient rule example 2
x^5/x^3= x^2
Power of a power definition
taking an expression that is already raised to an exponent and raising it to yet another exponent
Power of a power formula
(a^m)^n = a^mn
Power of a power example 1
(3^2)^4 =3 x 3 x 3 x 3 = 81 =81^(2 x 4) = 81 ^8
Power of a power example 2
(2^4)^2 = 2 x 2 = 4 = 4^(4 x 2) = 4^8
Power of a product definition
one raised to the power of anything is one
Power of a product formula
1^n = 1
Power of a product example 1
1^7 = 1
Power of a product example 2
1^40 = 1
Power of a Quotient definition
another way you can simplify an algebraic equation with exponents; if there is more than one term in parenthesis, with an exponent outside the parenthesis then the exponent is distributes to every term in the parenthesis
Power of a quotient formula
(m/n)^5=m^5/n^5
Power of a quotient example 1
(a/b)^7 = a^7/b^7
Power of a quotient example 2
(2x/y)^3 = 8x^3/y^3
Zero exponent definition
tells the problem solver to multiply the number zero times by itself, any base with an exponent of zero is equal to one
Zero exponent formula
n^0 = 1
Zero exponent example 1
24^0 = 1
Zero exponent example 2
46^0 = 1
Negative exponent definition
A negative exponent means how many times to divide the number by
Negative exponent formula
a^-n = 1/a^n
Negative exponent example 1
4^-2 = 1/16
Negative exponent example 2
10^-3 = .001
Rational exponent definition
The use of rational numbers as exponents
Rational exponent formula
b^(1/n) = n(sqr root)b
Rational exponent example 1
36^(3/2) = 216
Rational exponent example 2
27^(4/3) = 81
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