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Q: How do you find the prime factorization of 900 using exponents?

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24*3

(a) what is the prime factorization of 5184 using exponents? (b)Use the answer (a) to find the square root of 5184

36 = 22 × 32

48 = 24 × 3

As a product of its prime factors using exponents: 2^3 times 3 times 5 = 120

Find the prime factorization of the number 32 use exponents when possible

42=2^3*7

48 = 24 × 3

The prime factorization of 90 with exponents is: 2 x 32 x 5

321 = 3*107

2^3 x 3 = 24

24 x 3 = 48

112 = 121

The prime factorization of 44 is 2 x 2 x 11 or, in index form (in other words, using exponents), 22x11

22 x 3 x 5 = 60

5 x 72 = 245

10^6 = 2^6 x 5^6

Exponents are a way to notate repeated factors. The prime factorization of 72 is 2 x 2 x 2 x 3 x 3. Using exponents, that's 2^3 x 3^2.

2.2.3 and

3^2 x 5 = 45

I assume you mean to find the prime factorization of 405. If so: 34 x 5

To find the prime factorization of a number, it helps to divide it by any obvious factors. In this case, 156 is even so we can divide by 2. Do this and we get 78, which is also even. Divide by 2 again and we get 39, which is divisible by 3. Do that and we get 13 which is prime. Thus the prime factorization of 156 is 2x2x3x13. If we want to use exponents this can be written as 22x3x13

The prime factorization.

Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors.

Count the number of repeated factors. The prime factorization of 72 is 2 x 2 x 2 x 3 x 3 With exponents, that's 2^3 x 3^2