Question

simplify (2^n+3- 2*2^n)/2^n+3 step by step

​

Answer 1

$Given \: \frac{(2^{n+3} - 2\times 2^{n})}{2^{n+3}}$

$= \frac{(2^{n} \times 2^{3} - 2\times 2^{n})}{2^{n} \times 2^{3}}$

$= \frac{ \cancel {2^{n}} ( 2^{3} - 2 )}{\cancel { 2^{n} }\times 2^{3}}$

$= \frac{(8 - 2 )}{8}$

$= \frac{6}{8}$

$= \frac{3}{4}$

Therefore.,

$\red{\frac{(2^{n+3} - 2\times 2^{n})}{2^{n+3}}}$

$\green { = \frac{3}{4}}$

•••♪

Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Equation : }}}$

$\:$

• $\footnotesize{ \dfrac{2^n+3 - 2 \times 2^n}{2^{n+3}}}$

$\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Formula \: used : }}}$

$\:$

• $\footnotesize{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

• $\footnotesize{ab + ac = a( b + c)}$

$\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution : }}}$

$\:$

$\footnotesize{ \dfrac{2^{n+3} - 2 \times 2^n}{2^{n+3}}}$

$\footnotesize{= \dfrac{2^n \times 2^3 - 2 \times 2^n}{2^n \times 2^3}}$

$\footnotesize{= \dfrac{2^n ( 2^3 - 2)}{2^n \times 2^3}}$

$\footnotesize{= \dfrac{ 8 - 2}{ 8}}$

$\footnotesize{= \dfrac{ 6}{ 8}}$

$\footnotesize{= \dfrac{3}{4}}$

$\:$

$\bold{Answer = \dfrac{3}{4}}$