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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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