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Law of Exponents

Use the laws of exponents to simplify expressions, including those with rational exponents.

$a^{m},\ a^{n}=a^{m+n}$
$(a^{m})^{n}=a^{mn}$
$a^{-m}=\frac{1}{a^{m}}$
$a^{\frac{1}{n}}=\sqrt[n]{a^1}$
$\frac{a^m}{a^n}=a^{m-n}$

Simplify: $\frac{a(a^{3}b^{2})}{(a^{3})^{2}}=\frac{a^{4}b^{2}}{a^6}=\frac{a\cdot a\cdot a\cdot a\cdot b\cdot b}{a\cdot a\cdot a\cdot a\cdot a\cdot a}=\frac{b^2}{a^2}$

Simplify: $36^{\frac{1}{2}}=\sqrt[2]{36^1}=\sqrt{36}=6\rightarrow 6\times 6$