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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