Question

simplify (3^-5)^2×3^-3/3^-2÷3^4​

Answer 1

Question

$\dfrac{(3^{-5})^{2}\times 3^{-3}}{3^{-2}\div 3^{4}}$

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Answer

$\dfrac{(3^{-5})^{2}\times 3^{-3}}{3^{-2}\div 3^{4}}$

Laws of Exponent to be used →

• $(a^{m})^{n} = a^{m\times n}$
• $a^{m} \div a^{n} = a^{m-n}$

⇒ $\dfrac{(3^{-5})^{2}\times 3^{-3}}{3^{-2}\div 3^{4}}$

⇒ $\dfrac{3^{-5\times 2}\times 3^{-3}}{3^{-2-4}}$

⇒ $\dfrac{3^{-10}\times 3^{-3}}{3^{-6}}$

Law of Exponent to be used →

• $a^{m}\times a^{n} = a^{m+n}$

⇒ $\dfrac{3^{-10+-3}}{3^{-6}}$

⇒ $\dfrac{3^{-10-3}}{3^{-6}}$

⇒ $\dfrac{3^{-13}}{3^{-6}}$

Law of Exponent to be used →

• $\dfrac{a^m}{a^n} = a^{m-n}$

⇒ $3^{-13-(-6)}$

⇒ $3^{-13+6}$

⇒ $3^{-7}$

Law of Exponent to be used →

• $a^{-m}=\dfrac{1}{a^{m}}$

⇒ $\dfrac{1}{3^{7}}$

$\bf \therefore \dfrac{(3^{-5})^{2}\times 3^{-3}}{3^{-2}\div 3^{4}} = 3^{-7} \ (or) \ \dfrac{1}{3^{7}}$

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Answer 2

Answer:

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