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Exponent Laws & Rules

Examples using some of the exponential rules

For example:

\begin{eqnarray*}
\frac{8a^{-2}}{a^3} &=& \frac{8}{a^{2}\times a^{3}} \\
&=&\frac{8}{a^5}
\end{eqnarray*}
And another example:
\begin{eqnarray*}
\frac{8\left(a^3b^6\right)^{-\frac{1}{3}}}{b^{-5}} & = & \frac{8\left(a^3\right)^{-\frac{1}{3}}\left(b^6\right)^{-\frac{1}{3}}}{b^{-5}} \\
& = & \frac{8a^{-1}b^{-2}}{b^{-5}} \\
& = & 8a^{-1}b^{-2-(-5)} \\
& = & 8 \times \frac{1}{a} \times b^{-2+5} \\
& = & \frac{8}{a}\times b^3 \\
& = & \frac{8b^3}{a}
\end{eqnarray*}