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Chapter 10: Problem 32

Compute ([7]73) \(^{15}\) by raising 7 to the \(15^{\text {th }}\) power

Short Answer

Expert verified
The result of \(7^{15}\) is quite large, so it's best to use a calculator for the exact value. If done correctly, one will get \(7^{15} = 4747561509943\).

Step by step solution

01

Understanding the power notation

The term \(7^{15}\) represents the number 7 multiplied by itself 15 times.
02

Performing the exponentiation operation

To compute the value of \(7^{15}\), one needs to multiply 7 by itself 15 times, which can either be done by long multiplication or using a calculator to ensure accuracy and efficiency.

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Most popular questions from this chapter

Find the positive divisors of the following integers. a. 72 b. 31 c. 123

Find all solutions to the equations \([1]_{7} x=[3]_{7}\) and \([12]_{9} x=[6]_{9}\).

Consider an RSA cryptosystem using \(p=23, q=\) 41 and \(g=3 .\) Encipher the message \([847]_{943}\).

Prove that if \(s \in[m]_{n}\) and \(t \in[k]_{n}\) then \(s \times t \in[m\) \(\times k] n\).

Show that if \(\left.S=\\{[0]\\}_{12},[3]_{12},[6]_{12},[9]_{12}\right\\},\) then \((S,+)\) is a subgroup of \(\left(\mathbf{Z}_{12},+\right)\).
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