Question

Which equation applies the associative property of multiplication? ​(−14−53)−35=−14−(53−35)​ ​ (−78⋅25)+(−78⋅35)=−78⋅(25+35) ​ ​ −512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92) ​ ​ −67⋅811⋅13=811⋅(−67)⋅13 ​

Answer 1

It is the third equation: −512⋅(65⋅13)⋅92=(−512⋅65)⋅(13⋅92)

Associative property means one can group the individual operations arbitrarily without changing the result.

Answer 2

The correct answer option is −512⋅(65⋅13)⋅92 = (−512⋅65)⋅(13⋅92).

Explanation:

The associative property of multiplication states that when multiplying three or more (real) numbers, their result must be the same despite of their arrangement or the sequence in which they are grouped.

So the equation must give the same result in whatever way they are grouped. By grouping, we are referring to the use of brackets or parenthesis here.

Solving −512⋅(65⋅13)⋅92 gives us a result of -39802880

and solving (−512⋅65)⋅(13⋅92) also gives us -39802880 which means they are equal. Therefore, the associative property of multiplication is valid for the equation −512⋅(65⋅13)⋅92 = (−512⋅65)⋅(13⋅92).