Algebra Test 5-1, 5-3, 5-4, 6-1, 6-2

Power of a Quotient

(a/b)^m= (a^m)/(b^m)

Product of Powers

when multiplying like bases add the exponents ( a^2 )(a^3) = a^5

Power of a Power

when raising a power to a power multiply exponents (a^2)^3= a^6

n is even integer 1. a<0 2. a=0 3. a>0

1. no real nth roots 2. one real nth root: 3. two real nth roots:

n is odd integer 1. a<0 2. a=0 3. a>0

1. one real nth root: 2. one real nth root: 3. one real nth root:

Negative Exponents

Raising a number to a negative exponent is the same as raising the number's reciprocal to the equivalent positive exponent. {a^-2 = 1/a^2} {1/a^-2 = a^2}

radical exponent notation

a^m/n= (a^1/n)^m= ()^m

Quotient of Powers

for all integers m and n and any nonzero number a, a^m/ a^n = a^m - ^n

Power of a Product

for all numbers a and b, and any integer m, (ab)^m = a^m X b^m

Zero Exponent

for any nonzero number a, a^0 =1