Question

Express the following in exponential form :
${\left(\frac{9}{2}\right)}^4$

Answer 1

${\left(\frac{9}{2}\right)}^4={\left(\frac{8+1}{2}\right)}^4\Rightarrow {(4+\frac{1}{2})}^4={(4+\frac{1}{2})}^2{(4+\frac{1}{2})}^2$

$=\left(\right(2^2{)}^2+2\times 2^2\times \frac{1}{2}+{\left(\frac{1}{2}\right)}^2{)}^2$

$=(2^4+2^2+2^{-2}{)}^2$

${\left(\frac{9}{2}\right)}^4=2^8+2^4+2^{-4}+{2.2}^4{.2}^2+{2.2}^2{2}^{-2}+{2.2}^4{.2}^{-2}$

$=2^8+2^4+2^{-4}+2^7+2+2^3$

${\left(\frac{9}{2}\right)}^4=2^8+2^7+2^4+2^3+2+2^{-4}$