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Chapter 14: Problem 10

By which of the following could \(10\left(9^{6}\right)\) be divided by to produce an integer result? Indicate all such values. a. 90 b. 100 c. 330 d. 540 e. 720

Short Answer

Expert verified
The value \(10(9^{6})\) is divisible by option a, which is 90, and no other options.

Step by step solution

01

Calculate the value of \(10(9^{6})\)

The first step is to calculate the value of \(10(9^{6})\). To do this, raise 9 to the power of 6, and then multiply the result by 10. This gives us \(10(531441) = 5314410\).
02

Determine divisibility by potential factors

The next step involves testing each of the given options to see if \(5314410\) divided by the option results in an integer. For option a, \(5314410 / 90 = 59049\) which is an integer. For option b, \(5314410 / 100 = 53144.1\) which is not an integer. For option c, \(5314410 / 330 = 16104.2727\) which is not an integer. For option d, \(5314410 / 540 = 9837.80556\) which is not an integer. For option e, \(5314410 / 720 = 7381.125\) which is not an integer.

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