Question

$$( ) ( \frac { 2 } { 3 } ) ^ { 5 } = \frac { 2 } { 3 }$$

Answer

$$x=-23^(5-Bo)*IM$$

Solution


Remove parentheses.
\[\imath \imath \imath \times {23}^{5}={23}^{Bo}x\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{\imath }^{3}\times {23}^{5}={23}^{Bo}x\]
Isolate \({\imath }^{2}\).
\[{\imath }^{2}\imath \times {23}^{5}={23}^{Bo}x\]
Use Square Rule: \({i}^{2}=-1\).
\[-1\times \imath \times {23}^{5}={23}^{Bo}x\]
Simplify  \(1\times \imath \times {23}^{5}\)  to  \(\imath \times {23}^{5}\).
\[-\imath \times {23}^{5}={23}^{Bo}x\]
Regroup terms.
\[-{23}^{5}\imath ={23}^{Bo}x\]
Divide both sides by \({23}^{Bo}\).
\[-\frac{{23}^{5}\imath }{{23}^{Bo}}=x\]
Simplify  \(\frac{{23}^{5}\imath }{{23}^{Bo}}\)  to  \({23}^{5-Bo}\imath \).
\[-{23}^{5-Bo}\imath =x\]
Switch sides.
\[x=-{23}^{5-Bo}\imath \]