Simplify- - 7-6 -5- 6-7 -3 -

The correct option is A ( 7/6 )^ 2 [ (7/6 #160; )^ 5× ( 6/7 )^ 3 ]=7^ 5/6^ 5×6^ 3/7^ 3 =7^ 2/6^ 2 = (7/6 #160; )^ 2 ...

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Byju's Answer

Standard VIII

Mathematics

Powers with Negative Exponents

Simplify: [...

Question

Simplify: $[{(\frac{7}{6})}^{- 5} \times {(\frac{6}{7})}^{- 3}]$

{(\frac{7}{6})}^{- 2}

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{(\frac{6}{7})}^{- 2}

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{(\frac{7}{6})}^{- 8}

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{(\frac{6}{7})}^{- 8}

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Solution

The correct option is A ${(\frac{7}{6})}^{- 2}$
$[{(\frac{7}{6})}^{- 5} \times {(\frac{6}{7})}^{- 3}] = \frac{7^{- 5}}{6^{- 5}} \times \frac{6^{- 3}}{7^{- 3}}$
$= \frac{7^{- 2}}{6^{- 2}}$
$= {(\frac{7}{6})}^{- 2}$

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Similar questions

Q. Simplify

(\frac{6}{7})^{- 2} \times (\frac{7}{6})^{- 2}

Q. How many 7's are there in the following series which are preceded by 6 which is not preceded by 8 ?
8 7 6 7 8 6 7 5 6 7 9 7 6 1 6 7 7 6 8 8 6 9 7 6 8 7

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Q. Which of the following will come next in the following series?

919829873987649876559876546987654

Q. 4+7+2=281435
7+3+9=212781
6+2+7=121456
2+8+5=164036
8+4+6=?????

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Simplify: [(76)−5×(67)−3]

The correct option is A (76)−2[(76)−5×(67)−3]=7−56−5×6−37−3=7−26−2=(76)−2

Simplify: $[{(\frac{7}{6})}^{- 5} \times {(\frac{6}{7})}^{- 3}]$

The correct option is A ${(\frac{7}{6})}^{- 2}$
$[{(\frac{7}{6})}^{- 5} \times {(\frac{6}{7})}^{- 3}] = \frac{7^{- 5}}{6^{- 5}} \times \frac{6^{- 3}}{7^{- 3}}$
$= \frac{7^{- 2}}{6^{- 2}}$
$= {(\frac{7}{6})}^{- 2}$