Solved on Dec 14, 2023

Find the prime factorization of 72 using exponential notation: 23322^{3} \cdot 3^{2}

STEP 1

Assumptions
1. We need to find the prime factorization of 72.
2. Prime factorization is expressing a number as the product of its prime factors.
3. Exponential notation means using exponents to show how many times a prime number is used as a factor.

STEP 2

Begin by writing 72 as a product of any two factors.
72=8×972 = 8 \times 9

STEP 3

Notice that neither 8 nor 9 is a prime number, so we need to further factorize both numbers.

STEP 4

Factorize 8 into prime factors.
8=2×48 = 2 \times 4

STEP 5

Further factorize 4, which is a factor of 8.
4=2×24 = 2 \times 2

STEP 6

Combine the factors of 8 into prime factors using exponential notation.
8=2×2×2=238 = 2 \times 2 \times 2 = 2^{3}

STEP 7

Now, factorize 9 into prime factors.
9=3×39 = 3 \times 3

STEP 8

Write 9 as a prime factor using exponential notation.
9=3×3=329 = 3 \times 3 = 3^{2}

STEP 9

Combine the prime factors of 8 and 9 to express 72 as a product of prime factors.
72=23×3272 = 2^{3} \times 3^{2}

STEP 10

Compare the result with the given options.
The correct prime factorization of 72 using exponential notation is 23322^{3} \cdot 3^{2}.

Was this helpful?
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ContactInfluencer programPolicyTerms
TwitterInstagramFacebookTikTokDiscord