Question

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Evaluate:-
[(1/4)^-1 - (1/5)^-1]^-1]
Ch-Exponents and powers
Class-8th
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Answer 1

Question:-

$\mapsto$ Evaluate $\sf \{ ({ \frac{1}{4}) }^{ - 1} - {( \frac{1}{5}) }^{ - 1} \}^{ - 1}$

Answer:-

$\mapsto$ The answer is -1

Solution:-

$\sf \{ ({ \frac{1}{4}) }^{ - 1} - {( \frac{1}{5}) }^{ - 1} \}^{ - 1}$

$\sf = \{4 - 5 \}^{ - 1}$

$\sf = { - 1}^{ - 1}$

$\sf = - 1$

Formulae Used:-

$\sf \mapsto {a}^{ - b} = \frac{1}{ {a}^{b} }$

Answer 2

$[(\dfrac{1}{4})^{-1} - (\dfrac{1}{5})^{-1}]^{-1}$

We will apply the negative power law here.

Negative Power Rule ⇒ m⁻¹ = ¹/m

⇒ $[(\dfrac{1}{4})^{-1} - (\dfrac{1}{5})^{-1}]^{-1}$

⇒ $[4^{1} - 5^{1}]^{-1}$

⇒ $[4 - 5]^{-1}$

Now we will subtract numbers in the box bracket.

⇒ $[4 - 5]^{-1}$

⇒ $[-1]^{-1}$

We will apply the negative power law here.

Negative Power Rule ⇒ m⁻¹ = ¹/m

⇒ $[-1]^{-1}$

⇒ $\dfrac{1}{-1}$

⇒ -1

$\bf \therefore [(\dfrac{1}{4})^{-1} - (\dfrac{1}{5})^{-1}]^{-1} = -1$