Rules of Exponents
Definition of Base
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The base of an exponent is a number which is raised to a certain power, The base represents the number or variable that is multiplied by itself,
An example:
38,,,in this case, 3 would be the base,
Definition of Exponent
⯆
The exponent of a base represents how many times that number if multiplied by itself, it is written as a small number to the top right of the base number,
An Example:
38,,,in this case, 8 would be the exponent,
Power of Zero
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Any base to the power of 0 will always result in 1, This is because a number divided by itself is 1, A base to the power of zero is equivilant to this,
An Example:
30 = 3/3 = 1
Negative Exponents
When an exponent is negative the power is made positive and dropped into the denominator of a fraction,
An Example:
3-2 = 1/32
Multiplying Powers
When the bases of the exponents being multiplied are the same, the exponents are added together,
An Example:
32 x 31 = 93
Power to a Power
When the bases of the exponents being multiplied are the same, the exponents are added together,
An Example:
32 x 31 = 93
Power of a Product
When bases are being multiplied inside a parentheses set with an exponent on the outside, the exponent is carried to every base, If one of teh bases already has an exponent it is multiplied by the outside exponent,
An Example:
(x2 c)2 = x42c
Diving Powers
When there are powers in the denominator and numerator of a fraction with the same base the exponents are subtracted from the other,
An Example:
x6/x2=x4
Power of a Quotient
If a fraction is in parentheses and has an exponent outside the parentheses the exponent is distributed to every part of the fraction,
An Example:
(x/a)2=x2/a2