Well, let's take a moment to appreciate the number 240. If we break it down into its prime factors, we get 2 x 2 x 2 x 2 x 3 x 5. In index form, this would be written as 2^4 x 3 x 5. Isn't it wonderful how numbers can be broken down into their simplest, most beautiful form?
It is: 23*3*52 = 600
To express 144 as a product of its prime factors in index form, we first find the prime factors of 144, which are 2 and 3. 144 can be written as 2^4 * 3^2 in index form, where 2 is raised to the power of 4 and 3 is raised to the power of 2. This shows that 144 can be expressed as the product of its prime factors in index form.
To express 36 as a product of prime factors, we first break it down into its prime factors: 2 x 2 x 3 x 3. This simplifies to 2^2 x 3^2 in index form, where the exponents represent the number of times each prime factor is multiplied.
180 = 2 x 2 x 3 x 3 x 5 or 22 x 32 x 5
2^2 x 3 x 5
It is: 23*3*52 = 600
648 expressed as a product of its prime factors in index form is 2^3 times 3^4
To express 375 in prime factor index form, first, factor it into its prime components. The prime factorization of 375 is (3 \times 5^3) because (375 = 3 \times 125) and (125 = 5^3). Therefore, the prime factor index form of 375 is (3^1 \times 5^3).
300
To express 600 as a product of its prime factors in index form, we first find its prime factorization. The prime factors of 600 are 2, 3, and 5. Specifically, 600 can be expressed as (2^3 \times 3^1 \times 5^2). Thus, in index form, 600 is represented as (2^3 \times 3^1 \times 5^2).
32 x 19
To express 63 as a product of prime factors in index form, we first need to find the prime factors of 63. 63 can be factored as 3 x 3 x 7. This can be written in index form as 3^2 x 7. Therefore, 63 as a product of prime factors in index form is 3^2 x 7.
72 *23
As a product of its prime factors: 5^3 times 13 = 1625
23 x 53 = 1000
22 x 3 = 12
To express 144 as a product of its prime factors in index form, we first find the prime factors of 144, which are 2 and 3. 144 can be written as 2^4 * 3^2 in index form, where 2 is raised to the power of 4 and 3 is raised to the power of 2. This shows that 144 can be expressed as the product of its prime factors in index form.