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search-thumbnail-We know that $\left(a^{m}\right)^{n}=a^{mn}$ 
Let $a^{m}=x$ then $x$ $m=log _{a}$ 
$x^{n}=a^{mn}$ then $x^{n}=mn$ $log _{a}$ 
$x$ $=nlog _{a}$ $\left($ (why?)
10th-13th grade
Other
search-thumbnail-$\left(a\right)$ $a^{m}\times a^{n}=a^{m+n}$ 
$\left(b\right)$ $a^{m}\div a^{n}=a^{m-n}$ $,$ $m>n$ 
(c) $\left(a^{m}\right)^{n}=a^{mn}$ 
(d) $a^{m}\times bm=\left(ab\right)^{m}$
7th-9th grade
Other
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