Question

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Answer 1

Step-by-step explanation:

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Answer 2

Solution!!

$\sf \to \dfrac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}$

$\sf \to \dfrac{3^{5}\times (2\times 5)^{5}\times (5)^{2}}{5^{7}\times (2\times 3)^{5}}$

$\sf \to \dfrac{3^{5}\times 2^{5}\times 5^{5}\times 5^{2}}{5^{7}\times 2^{5}\times 3^{5}}$

Product rule of exponents has to be used. Product rule → $\sf a^{m}.a^{n}=a^{m+n}$

$\sf \to \dfrac{3^{5}\times 2^{5}\times 5^{5+2}}{5^{7}\times 2^{5}\times 3^{5}}$

$\sf \to \dfrac{\cancel{3^{5}}\times \cancel{2^{5}}\times \cancel{5^{7}}}{\cancel{5^{7}}\times \cancel{2^{5}}\times \cancel{3^{5}}}$

$\sf \to 1$

You can also use the quotient rule of exponents instead of cancelling the terms.

Quotient rule → $\sf \dfrac{a^{m}}{a^{n}}=a^{m-n}$

$\sf \to \dfrac{3^{5}\times 2^{5}\times 5^{7}}{5^{7}\times 2^{5}\times 3^{5}}$

$\sf \to 3^{5-5}\times 2^{5-5}\times 5^{7-7}$

$\sf \to 3^{0}\times 2^{0}\times 5^{0}$

We know that a⁰ is always 1.

$\sf \to 1\times 1\times 1$

$\sf \to 1$