The correct options are A 1/25^3 B ( 25)^ 3We know that a^m × b^m=(ab)^m for non zero integers a and b, and any integer m. ∴ nbsp;5^ 3× ( 5)^ 3=(5× 5)^ 3 =( ...

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Byju's Answer

Standard IX

Mathematics

Exponent

5-3×-5-3=

Question

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

- \frac{1}{25^{3}}

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(- 25)^{- 3}

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25^{- 3}

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Solution

The correct options are
A $- \frac{1}{25^{3}}$
B $(- 25)^{- 3}$
We know that $a^{m} \times b^{m} = (a b)^{m}$ for non-zero integers $a$ and $b$ , and any integer $m .$
$∴ 5^{- 3} \times (- 5)^{- 3} = (5 \times - 5)^{- 3}$
$= (- 25)^{- 3}$
$= \frac{1}{(- 25)^{3}} (∵ a^{- m} = \frac{1}{a^{m}})$
$= - \frac{1}{25^{3}}$

Suggest Corrections

5−3×(−5)−3=

The correct options are A −1253 B (−25)−3We know that am×bm=(ab)m for non-zero integers a and b, and any integer m. ∴5−3×(−5)−3=(5×−5)−3 =(−25)−3 =1(−25)3 (∵a−m=1am) =−1253

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