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# 7. Simplify. (ii) (3^-5*10^-5*125)/5^-7*6^-5

Q7. Simplify.

(ii) $\frac{3^{-5}\times 10^{-5}\times 125}{5^{-7}\times6 ^{-5}}$

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The detailed solution for the above-written question is

$\frac{3^{-5}\times 10^{-5}\times 125}{5^{-7}\times6 ^{-5}}$

we can write 125 = $5^{3}$ and $6^{-5}$ can be written as $(2\times 3)^{-5}$

Now, rewriting the equation, we get

$=\frac{3^{-5}\times 10^{-5}\times 5^{3}}{5^{-7}\times(2\times 3) ^{-5}}$

$=\frac{3^{-5}\times 10^{-5}\times 5^{3+7}}{(2\times 3) ^{-5}}$.............by using $[a^{m}\div a^{n}=a^{m-n}]$

$=\frac{ 10^{-5}\times 5^{10}}{(2) ^{-5}}$  .....................Use $[a^{m}\div a^{n}=a^{m-n}]$

$5^{10-5}= 5^{5}=3125$.........................As $[10^{-5} = (2\times 5)^{-5}=2^{-5}\times 5^{-5}]$ . $2^{-5}$ can be cancelled out with the denominator $2^{-5}$

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