Question

evaluate: 3^3001+2999/3^3000-3​

Answer 1

I hope this will help you dear..

Always stay safe and stay healthy..

Answer 2

Answer:

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

$\dashrightarrow\sf\:\:\dfrac{\large{3^{3001}+3^{2999}}}{\large{3^{3001}-3^{2999}}}\\\\\\\dashrightarrow\sf\:\:\dfrac{\large{3^{(3000 + 1)}+3^{(3000 - 1)}}}{\large{3^{(3000 + 1)}-3^{(3000 - 1)}}}\\\\\\\dashrightarrow\sf\:\:\dfrac{\large{(3^{3000} \times 3^1)+(3^{3000} \times 3^{- 1})}}{\large{(3^{3000} \times 3^1)-(3^{3000} \times 3^{- 1})}}\\\\\\\dashrightarrow\sf\:\:\dfrac{\large{3^{3000}(3^1 + 3^{- 1})}}{\large{3^{3000}(3^1 - 3^{- 1})}}\\\\\\\dashrightarrow\sf\:\:\dfrac{\large{(3^1 + 3^{- 1})}}{\large{(3^1 - 3^{- 1})}}\\\\\\\dashrightarrow\sf\:\:\dfrac{\large{3 + \frac{1}{3}}}{\large{3 - \frac{1}{3}}}\\\\\\\dashrightarrow\sf\:\:\dfrac{\:\:\dfrac{9 + 1}{3}\:\:}{\dfrac{9 - 1}{3}}\\\\\\\dashrightarrow\sf\:\:\dfrac{10}{3} \times \dfrac{3}{8}\\\\\\\dashrightarrow\sf\:\: \dfrac{5}{4}\\\\\\\dashrightarrow\sf\:\:1 \dfrac{1}{4}$

⠀

How to approach exponential questions?

• First remember all the exponential rules given below.
• If power is negative, then to change it into positive. We reciprocate base number.
• If power is zero, it equals to 1
• If power is in fraction, try to find power of base which can cancel denominator. Like that question can be easy.

$\rule{200px}{.3ex}$

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