Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter R - Section R.1 - Factors and the Least Common Multiple - Exercise Set - Page R-7: 27

Answer

$81 = 3\cdot 3\cdot 3\cdot 3$

Work Step by Step

The $\textit{prime factorization}$ of a number is obtained by writing the number as a product of primes. To determine the prime factorization of $81$ we write the number as a product of factors and continue the process until all factors are prime numbers. We start by writing $81$ as a product of two numbers: $81=3\cdot 27$. The number $3$ is prime, but $27$ is not. So we write $27=3\cdot 9$: $81=3\cdot 3\cdot 9$. As $9$ is not a prime number we write: $9=3\cdot 3$ and we have: $81=3\cdot 3\cdot 3\cdot 3$. Now each factor is a prime number, therefore the prime factorization of $81$ is $3\cdot 3\cdot 3\cdot 3$.
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