Question

{(2^x+4 - 2^5 * 2^x) / 2*2^x+3} - 2^-3

Answer 1

Solution :

{(2^x+4 - 2^5 * 2^x) / 2*2^x+3} - 2^-3

= {(2^x+4 - 2^x+5) / 2*2^x+3} - 2^-3

[ 2^5 × 2^x = 2^x+5 ]

[ 2×2^x+3 = 2^x+4 ]

= {(2^x+4 - 2^x+5) / 2^x+4 } - 2^-3

Taking 2^(x+4) common from both the numerator and the denominator

= { 2^(x+4) × [ 1 - 2 ] } / { 2^(x+4) } - 2^-3

2^(x+4) cancels

= -1 - 1/8

= -9/8

This is the required answer

Additional Information ;

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$