Product of like bases:

To multiply powers with the same base, add the exponents and keep the common base.

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

So, x²x³ = x⁽²⁺³⁾ = x⁵

Quotient of like bases: 

To divide powers with the same base, subtract the exponents and keep the common base. 

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

So, x⁴/x² = x^(4-2) = x²

 Power to a power:   

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

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

So (x³)⁴ = x^3×4 = x¹²

Product to a power:

 To raise a product to a power, raise each factor to the power. 

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

 Quotient to a power:

To raise a quotient to a power, raise the numerator and the denominator to the power.

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

 Zero Exponent:

 Any number raised to the zero power is equal to “1”.

Example: x²/x² = x^2-2 = x⁰ =1

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”!