Exponents Review
Exponents Review
Powers: exponent
Xn
base
Law of Exponents:
1. Multiplication Law
xa * xb = xa+b
ex:
y5 * y7 = y5+7 = y12
22 * 2 = 22+1 = 23 = 8
2. Division Law
xa = xa-b
xb
ex:
d5 ÷ d2 = d5-2 = d3
1012 ÷ 108 = 1012-8 = 104 = 10000
3. Power Law
(xa)b = xa*b
ex:
(c3)5 = c3*5 = c15
(58)2 = 58*2 = 516
4. Power of a: Product Law
(xy)a = xayb
ex:
(mn)3 = m3n3
(4x)2 = 42x2 = 16x2
5. Power of a: Quotient Law
[pic]
ex:
[pic]
Zero Exponents:
- any based with an exponent of 0 equals one
ex:
(bv)0 = b0v0 = 1(1) = 1
Negative Exponents:
- if an exponent is negative, remove the negative exponent by turning the power into a fraction
x-b = 1 .
xb
x-2
1. make the base the denominator and the numerator is one
1 .
x
2. the negative exponent becomes positive and stays with the base in the denominator
1 .
x2
3. solve regularly
1 .
4
- to do the opposite (make a fraction into an exponent) take the denominator and turn it into the power base and make the exponent negative
1 . = x-b
xb
ex:
1. = x-4
x4
Fractional Exponents:
- to remove a fractional exponent, do the following
xa/b = √ xa
42/3
1. the denominator in the fractional exponent becomes the index of the radical
42/3 ( [pic]
2. the base becomes the radicant
42/3 ( [pic]
3. the numerator in the fractional exponent becomes the exponent in the radicant
42/3 ( [pic]
4. solve the radical problem
42/3 ( [pic] ( [pic] = 2
Scientific Notation:
- a number is written in the from of a x 10n, where 1 ≤ a ≤ 10 and n is an integer
1. if the exponent is positive, you move the decimal to the right
3.46 x 104 = 34,600
2. if the exponent is negative, you move the decimal to the left
1.89 x 10-2 = 0.0189
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