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

Definition
Example: x^{2}x^{3} = (xx)(xxx) = xxxxx = x^{5}
So, x^{2}x^{3} = x^{(2+3)} = x^{5}



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

Definition
Example: x^{4}/x^{2} = (xxxx) / (xx) = xx = x^{2}
So, x^{4}/x^{2} = x^{(42)} = x^{2} 


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

Definition
Example: (x^{3})^{4} = (xxx)^{4} = (xxx)(xxx)(xxx)(xxx) = xxxxxxxxxxxx = x^{12}
So (x^{3})^{4} = x^{3×4} = x^{12} 


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) = x^{3}y^{3} 


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) = x^{3}/y^{3} 


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


Definition
Example: x^{2}/x^{2} = x^{22} = x^{0} =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 


