Question

$(5 {}^{ - 1} \: - \: 10 {}^{ - 1} ) {}^{ - 3}$
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Answer 1

ANSWER:

To Solve:

• $\left(5^{-1}-10^{-1}\right)^{-3}$

Solution:

We are given that,

$\implies\left(5^{-1}-10^{-1}\right)^{-3}$

We know that,

$\hookrightarrow a^{-x}=\dfrac{1}{a^x}$

So,

$\implies\left(\dfrac{1}{5^1}-\dfrac{1}{10^1}\right)^{-3}$

So,

$\implies\left(\dfrac{1}{5}-\dfrac{1}{10}\right)^{-3}$

Taking LCM,

$\implies\left(\dfrac{2-1}{10}\right)^{-3}$

Hence,

$\implies\left(\dfrac{1}{10}\right)^{-3}$

But,

$\hookrightarrow a^{-x}=\dfrac{1}{a^x}$

So,

$\implies(10)^3$

$\implies 10\times10\times10$

Hence,

$\implies\bf 1000$

Therefore,

$\implies\bf\left(5^{-1}-10^{-1}\right)^{-3} =1000$