Properties of Exponents

Words: when multiplying like bases, add the exponents

Symbols: (x^a)(x^b) = x^a+b

Numbers: (8³)(8⁶) = 8⁹

Words: when a power (base with exponent) is raised to another power (exponent), you multiply the exponents (keep the base!)

Symbols: (x^a)^b= x^ab

Numbers: (8³)⁶=8¹⁸

Words: if two or more bases are grouped together in parentheses and raised to an exponent, each base is raised to that exponent.
Symbols:  $\left(xy\right)^2=x^2y^2$  

Numbers:

Words: when dividing like bases, subtract the exponents
Symbols:

Words: if a fraction is raised to an exponent, both the numerator and denominator are raised to that exponent
Symbols:   $\left(\frac{x}{y}\right)^3=\frac{x^3}{y^3}$  

Words: any number (except zero) raised to a power of zero is equal to 1
Symbols:   $n^0=1$