Question

$$\left. \begin{array} { l } { ( a ^ { 4 } ) ^ { 2 } \div ( a ^ { 3 } \times a ) = } \end{array} \right.$$

Answer

$$e^3*IM*a^8*s^2*f*r*c*t^2*o*n^3*d*h*u$$

Solution


Simplify  \({a}^{3}a\)  to  \({a}^{4}\).
\[easafract\imath onandthenuse\times \frac{{({a}^{4})}^{2}}{{a}^{4}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[easafract\imath onandthenuse\times \frac{{a}^{8}}{{a}^{4}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{easafract\imath onandthenuse{a}^{8}}{{a}^{4}}\]
Regroup terms.
\[\frac{aaaa{a}^{8}ssfrcttonnndhue\imath ee}{{a}^{4}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{a}^{1+1+1+1+8}{s}^{1+1}frc{t}^{1+1}o{n}^{1+1+1}dhue\imath ee}{{a}^{4}}\]
Simplify  \(1+1\)  to  \(2\).
\[\frac{{a}^{2+1+1+8}{s}^{1+1}frc{t}^{1+1}o{n}^{1+1+1}dhue\imath ee}{{a}^{4}}\]
Simplify  \(2+1\)  to  \(3\).
\[\frac{{a}^{3+1+8}{s}^{1+1}frc{t}^{1+1}o{n}^{1+1+1}dhue\imath ee}{{a}^{4}}\]
Simplify  \(3+1\)  to  \(4\).
\[\frac{{a}^{4+8}{s}^{1+1}frc{t}^{1+1}o{n}^{1+1+1}dhue\imath ee}{{a}^{4}}\]
Simplify  \(4+8\)  to  \(12\).
\[\frac{{a}^{12}{s}^{1+1}frc{t}^{1+1}o{n}^{1+1+1}dhue\imath ee}{{a}^{4}}\]
Simplify  \(1+1\)  to  \(2\).
\[\frac{{a}^{12}{s}^{2}frc{t}^{2}o{n}^{2+1}dhue\imath ee}{{a}^{4}}\]
Simplify  \(2+1\)  to  \(3\).
\[\frac{{a}^{12}{s}^{2}frc{t}^{2}o{n}^{3}dhue\imath ee}{{a}^{4}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{a}^{12}{s}^{2}frc{t}^{2}o{n}^{3}dhu{e}^{3}\imath }{{a}^{4}}\]
Regroup terms.
\[\frac{{e}^{3}\imath {a}^{12}{s}^{2}frc{t}^{2}o{n}^{3}dhu}{{a}^{4}}\]
Simplify.
\[{e}^{3}\imath {a}^{8}{s}^{2}frc{t}^{2}o{n}^{3}dhu\]