Question

(3^-5*10^-5*5^3)÷(5^-7*6^-5*5^5)​

Answer 1

ANSWER✔

$\sf\therefore \dfrac{3^{-5}\times 10^{-5} \times 5^{3}}{5^{-7} \times 6^{-5} \times 5^5}$

✯IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\:a^m \times b^m= (ab)^m \:\: \star}}}$

$\large{\boxed{\bf{ \star\:\:a^m \times a^n= (a)^{m+ n} \:\: \star}}}$

$\sf\implies \dfrac{3^{-5}\times 10^{-5} \times 5^{3}}{5^{-7} \times 6^{-5} \times 5^5}$

$\sf\implies \dfrac{30^{-5} \times 5^3}{5^{-7+5}\times 6^{-5}}\:-----\boxed{using\:given\: identities}$

$\sf\implies \dfrac{30^{-5} \times 5^3}{5^{-2} \times 6^{-5}}$

$\sf\implies \dfrac{\bigg(\dfrac{1}{30}\bigg)^5 \times 5^3}{\bigg( \dfrac{1}{5}\bigg)^2 \times \bigg( \dfrac{1}{6}\bigg)^5}$

$\sf\implies \dfrac{1}{30^5} \times 5^3 \times 5^2 \times 6^5$

$\sf\implies \dfrac{1}{30^5} \times 5^{3+2} \times 6^5$

$\sf\implies \dfrac{1}{30^5} \times 5^{5} \times 6^5$

$\sf\implies \dfrac{5^5\times 6^5}{30^5}$

$\sf\implies \dfrac{30^5}{30^5}$

$\sf\implies \cancel \dfrac{30^5}{30^5}$

$\sf\implies 1$

$\large{\boxed{\bf{ \star\:\:\implies 1 \:\: \star}}}$

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