Question

On simplifying 2^30 +2^29/2^31 - 2^30
i will report wrong answers and mark the answer brainliest if correct

Answer 1

Step-by-step explanation:

⇒ (2³⁰ + 2²⁹) / (2³¹ - 2³⁰)

⇒ (2²⁹⁺¹ + 2²⁹) / (2³⁰⁺¹ - 2³⁰)

⇒ (2.2²⁹ + 2²⁹) / (2.2³⁰ - 2³⁰)

⇒ 2²⁹(2 + 1) / 2³⁰(2 - 1)

⇒ 2²⁹(3) / 2³⁰(1)

⇒ 3. 2²⁹/2³⁰

⇒ 3.2²⁹⁻³⁰

⇒ 3.2⁻¹

⇒ 3/2  = 1.5

Answer 2

Answer:

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

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

$\rule{180}{1.5}$

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