Question

On simplifying 2^30 +2^29/2^31 - 2^30 we get​

Answer 1

Step-by-step explanation:

(2^30 - 2^30) + 2^{29 - 31}

=> 0 + 2^(-2)

=> 1 / 2^2

=> 1/4

The simplification result is = 1/4 .

Answer 2

Step-by-step explanation:

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{2^{30}+2^{29}}{2^{31}-2^{30}}\\\\\\:\implies\sf \dfrac{2^{29}\bigg\lgroup2^{1} + 1\bigg\rgroup}{2^{30}\bigg\lgroup2^{1} - 1\bigg\rgroup}\\\\\\:\implies\sf \dfrac{\bcancel{2^{29}}\bigg\lgroup2 + 1\bigg\rgroup}{\bcancel{2^{30}}\bigg\lgroup2 - 1\bigg\rgroup}\\\\\\:\implies\sf \dfrac{3}{2 \times 1}\\\\\\:\implies\sf \dfrac{3}{2}\\\\\\:\implies\underline{\boxed{\sf 1.5}}$

$\rule{180}{1.5}$

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