Properties of Exponents

Product Property: a^m \cdot a^n= a^{m+n}    and   (xy)^m=x^m \cdot y^m

Example: 2^6 \cdot 2^8=2^{14}    and   (2x)^{5}=2^5 \cdot x^5

 

Power Property:  \left(a^m \right)^n = a^{(m \cdot n)}

Example: \left(g^2\right)^3=g^6

 

Quotient Property: \frac{a^m}{a^n}=a^{m-n}

Example: \frac{k^7}{k^4} = k^3   and   \frac{k^2}{k^8}=k^{-6}

 

Negative Property: a^{-n}=\frac{1}{a^n}   and   \frac{1}{a^{-n}}=a^{n}

Example: 2^{-1}=\frac{1}{2}  and   \left(\frac{1}{2}\right)^{-1}=2   and   \left(\frac{2}{3}\right)^{-1}=\frac{3}{2}

 

Zero Property: a^0=1

Example: 555,987,123,987,123^0=1

 

Power of a Quotient Property: \left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}

Example: \left(\frac{2}{3}\right)^3=\frac{2^3}{3^3}=\frac{8}{27}