Final answer:
The number 252 in index form is 2^2 x 3^2 x 7. This expression is achieved by factorizing 252 into its prime factors and then using exponential notation to indicate repeated multiplication of the same factor.
Step-by-step explanation:
To express the number 252 in index form, also known as prime factorization, we need to break it down into its prime factors. The prime factors of a number are the prime numbers that multiply together to give the original number. The process of finding these factors is known as prime factorization.
Let's factorize 252:
- Divide 252 by the smallest prime number, which is 2.
252 ÷ 2 = 126 - Divide 126 by 2 again.
126 ÷ 2 = 63 - Now, 63 is not divisible by 2, so we try the next prime number, which is 3.
63 ÷ 3 = 21 - Divide 21 by 3 once more.
21 ÷ 3 = 7
Finally, 7 is a prime number and cannot be divided further.
Combining these prime factors, we get 2 x 2 x 3 x 3 x 7. In index form, this is written as 22 x 32 x 7.
Therefore, 252 expressed in index form is 22 x 32 x 7.