Question 71

In the following question, state whether the given statements are true (T) or false (F).

$(- 5)^{- 2} \times (- 5)^{- 3} = (- 5)^{- 6}$

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Solution

False:

$L H S = (- 5)^{- 2} \times (- 5)^{- 3}$

Using law of exponents ,
$a^{m} \times a^{n} = (a)^{m + n}$

$∴ (- 5)^{- 2} \times (- 5)^{- 3} = (- 5)^{- 2 - 3} = (- 5)^{- 5}$

Since, LHS is not equal to RHS, the given statement is false.

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Powers with Negative Exponents

Standard VIII Mathematics

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Question 71 In the following question, state whether the given statements are true (T) or false (F). (−5)−2×(−5)−3=(−5)−6

False: LHS=(−5)−2×(−5)−3 Using law of exponents , am×an=(a)m+n ∴(−5)−2×(−5)−3=(−5)−2−3=(−5)−5 Since, LHS is not equal to RHS, the given statement is false.

Question 71

In the following question, state whether the given statements are true (T) or false (F).

$(- 5)^{- 2} \times (- 5)^{- 3} = (- 5)^{- 6}$

False:

$L H S = (- 5)^{- 2} \times (- 5)^{- 3}$

Using law of exponents ,
$a^{m} \times a^{n} = (a)^{m + n}$

$∴ (- 5)^{- 2} \times (- 5)^{- 3} = (- 5)^{- 2 - 3} = (- 5)^{- 5}$

Since, LHS is not equal to RHS, the given statement is false.