The Exponent Laws Rule Zero as an Exponent Negative Exponents Multiplication Division Power of a Power Power of a Product English Description When an exponent is zero, the value of the power is 1. When an exponent is negative take the reciprocal of the base and make the exponent positive. When multiplying exponents with the same base, keep the base and add the exponents. When dividing exponents with the same base, keep the base and subtract the exponents. When raising an exponent to an exponent, keep the base and multiply the exponents. A product raised to a power is equivalent to the product of each factor raised to the same power. Algebraic Description
x
0  1 ,
x
 0
x

n
 1
x n
,
x
 0   
x

y
  
n
   
y x
  
n x n

x m

x n

m x n

x m

x n

m
,
x
 0
x n x m

x n

m
,
x
 0  
m

x n

m
 
n

x n y n
Power of a Quotient Rational Exponents A quotient raised to a power is equivalent to the quotient of the numerator and the denominator each raised to the same power. When an exponent is a fraction, its denominator indicates the degree of the root.   
x

y
 
n x n

y n
'
y
 0
x n
1 
n x
,
x
 0 if n is even
x n m

n x m

n x m
,
x
 0 if n is even
x

m n

n
1
x m
,
x
 0 ,
x
 0 if n is even www.mostly-math.com
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