# Shared Flashcard Set

## Details

scientific notation
math
7
Mathematics
01/18/2012

Term
 Product of like bases: To multiply powers with the same base, add the exponents and keep the common base.
Definition

### Example: x2x3 = (xx)(xxx) = xxxxx = x5

So, x2x3 = x(2+3) = x5

Term
 Quotient of like bases:  To divide powers with the same base, subtract the exponents and keep the common base.
Definition

### Example: x4/x2 = (xxxx) / (xx) = xx = x2

So, x4/x2 = x(4-2) = x2

Term
 Power to a power:    To raise a power to a power, keep the base and multiply the exponents
Definition

### Example: (x3)4 = (xxx)4 = (xxx)(xxx)(xxx)(xxx) = xxxxxxxxxxxx = x12

So (x3)4 = x3×4 = x12

Term
 Product to a power:  To raise a product to a power, raise each factor to the power.
Definition

### Example: (xy)3 = (xy)(xy)(xy) = xyxyxy = xxxyyy = (xxx)(yyy) = x3y3

Term
 Quotient to a power: To raise a quotient to a power, raise the numerator and the denominator to the power.
Definition

### Example: (x/y)3 = (x/y)(x/y)(x/y) = (xxx)/(yyy) = x3/y3

Term
 Zero Exponent:  Any number raised to the zero power is equal to “1”.
Definition

### Example: x2/x2 = x2-2 = x0 =1

Term
 Negative exponent:      Negative exponents indicate reciprocation, with the exponent of the reciprocal becoming  positive.  You may want to think of it this way:  unhappy (negative) exponents will become  happy (positive) by having the base/exponent  pair  “switch floors”!
Definition
 x-1 = 1/x 4-1 = 1/4
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