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Without computing, determine which number is greater, [ ( − 4 ) ^4 ] ^5 or − [ ( 4 ^12 ) ^3 ] . Explain your reasoning.

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Answer:

  [ ( − 4 ) ^4 ] ^5 is greater

Step-by-step explanation:

You want to know the greater of the two numbers ...

  • [ ( − 4 ) ^4 ] ^5
  • − [ ( 4 ^12 ) ^3 ]

Comparison

The two numbers have different numbers of minus signs involved in the product. One of them has an even number of minus signs (20), so will be positive. The other has an odd number of minus signs (1), so will be negative.

The greater number is the positive number:

  [ ( − 4 ) ^4 ] ^5 = 4^20

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Additional comment

The lesser number is the negative number:

  -(4^36)

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