Question

simplify (2e^2/3)^3 * (9e^2)^3/2 / e^-3

Answer 1

Answer:

$\large \bold\red{ 8 {e}^{12} }$

Step-by-step explanation:

Given,

${ (\frac{2 {e}^{2} }{3}) }^{3} \times \frac{ {(9 {e}^{2}) }^{ \frac{3}{2} } }{ {e}^{ - 3} }$

Further Simplifying,

We get,

$= {( \frac{2}{3}) }^{3} \times {e}^{6} \times {9}^{ \frac{3}{2} } \times {e}^{(2 \times \frac{3}{2}) } \times {e}^{3} \\ \\ = \dfrac{8}{27} \times {( {3}^{2}) }^{ \frac{3}{2} } \times {e}^{(6 + 3)} \times {e}^{3} \\ \\ = \frac{8}{27} \times {3}^{3} \times {e}^{9} \times {e}^{3} \\ \\ = \dfrac{8}{27} \times 27 \times {e}^{(9 + 3)} \\ \\ = \large \bold{ 8 {e}^{12} }$

Properties Used :-

• ${x}^{m} \times {x}^{n} = {x}^{(m + n)}$
• ${x}^{m} \times {y}^{m} = {(xy)}^{m}$
• ${x}^{ - m} = \dfrac{1}{ {x}^{m} }$

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

Given »

$\tt{ (\frac{2 {e}^{2} }{3}) }^{3} \times \frac{ {(9 {e}^{2}) }^{ \frac{3}{2} } }{ {e}^{ - 3} }$

By Simplifying given equation , We get »

$\begin{lgathered}=\sf {( \frac{2}{3}) }^{3} \times {e}^{6} \times {9}^{ \frac{3}{2} } \times {e}^{(2 \times \frac{3}{2}) } \times {e}^{3} \\ \\ = \sf\dfrac{8}{27} \times {( {3}^{2}) }^{ \frac{3}{2} } \times {e}^{(6 + 3)} \times {e}^{3} \\ \\ =\sf \frac{8}{27} \times {3}^{3} \times {e}^{9} \times {e}^{3} \\ \\ =\sf \dfrac{8}{27} \times 27 \times {e}^{(9 + 3)} \\ \\ =\tt \bold{ 8 {e}^{12} }\end{lgathered}$