I need to check my answer... please help...
the prime factorization in powers of primes of the number: 16380.
5460 to the power of three
is this correct
5460 is not a prime number. You must keep dividing.
5460 = 10 * 546
~ 10 = 2*5
546 = 6 * 91
~ 6 = 2*3
91 = 7 * 13
So you have 2^2 * 3^2 * 5^1 * 7^1 * 13^1
To check the prime factorization of 16380, we will need to find its prime factors in powers of primes.
Step 1: Start by dividing the number by the smallest prime number, which is 2.
16380 ÷ 2 = 8190
Step 2: We continue dividing by 2 until we can no longer divide evenly.
8190 ÷ 2 = 4095
Step 3: Now, we try dividing by the next prime number, which is 3.
4095 ÷ 3 = 1365
Step 4: We continue dividing by 3 until we can no longer divide evenly.
1365 ÷ 3 = 455
Step 5: Next, we try dividing by the next prime number, which is 5.
455 ÷ 5 = 91
Step 6: We divide by 7, the next prime number.
91 ÷ 7 = 13
Step 7: Finally, we divide by 13.
13 ÷ 13 = 1
The prime factorization in powers of primes for 16380 is 2³ × 3 × 5 × 7 × 13.
To check if your answer is correct, we can calculate the prime factorization of 5460 and see if it matches.
To find the prime factorization of 5460, follow the same steps as above:
Step 1: Divide 5460 by 2.
5460 ÷ 2 = 2730
Step 2: Divide 2730 by 2.
2730 ÷ 2 = 1365
Step 3: Divide 1365 by 3.
1365 ÷ 3 = 455
Step 4: Divide 455 by 5.
455 ÷ 5 = 91
Step 5: Divide 91 by 7.
91 ÷ 7 = 13
Step 6: Divide 13 by 13.
13 ÷ 13 = 1
The prime factorization of 5460 is also 2³ × 3 × 5 × 7 × 13.
Therefore, your answer of 5460 to the power of three having a prime factorization of 2³ × 3 × 5 × 7 × 13 is correct.