Question

write the prime factorization of 49. use exponents when appropriate and order the factors from least to greatest (for example, $2^2 \cdot 3 \cdot 5$).

Explanation:

Step1: Identify prime factors of 49

49 is a composite number. We start by dividing it by the smallest prime number, which is 2. But 49 is odd, so it's not divisible by 2. Next prime number is 3. \(49\div3\) gives a non - integer result. Then we try 5, \(49\div5\) also gives a non - integer result. Now we try 7. \(49\div7 = 7\). And 7 is a prime number.

Step2: Write the prime factorization with exponents

Since we have two 7s (because \(7\times7 = 49\)), using exponents, we can write the prime factorization of 49 as \(7^{2}\).

Answer:

\(7^{2}\)