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Using Laws of Exponents

  1. a^{m}\times a^{n}=a^{m+n}
  2. (a^{m})^{n}=a^{mn}
  3. a^{-m}=\frac{1}{a^m}
  4. a^{\frac{1}{n}}=n\sqrt{a^1}
  5. \frac{a^m}{a^n}=a^{m-n}

 

Simplify: \frac{a(a^{3}b^{2})}{(a^{3})^{2}}

\frac{a(a^{3}b^{2})}{(a^{3})^{2}}=\frac{(a^{1}\times a^{3})b^{2}}{(a^{3})^{2}}=\frac{(a^{1+3})b^{2}}{(a^{3})^{2}}=\frac{a^{4}b^{2}}{a^{3\times2}}=\frac{a^{4}b^{2}}{a^6}=\frac{a\times a\times a\times a\times b\times b}{a\times a\times a\times a\times a\times a}=\frac{b^{2}}{a^{2}}

 

Simplify: 36^{\frac{1}{2}}

36^{\frac{1}{2}}=\sqrt[2]{36^{1}}=\sqrt{36}=6