Write 360 as powers of its prime factors
360 = 2*2*2*3*3*5
= (2^3)(3^2)(5)
To express 360 as powers of its prime factors, we need to identify the prime numbers that divide evenly into 360 and determine their exponents.
First, let's find the prime factors of 360:
Divide 360 by 2: 360 ÷ 2 = 180
Divide 180 by 2: 180 ÷ 2 = 90
Divide 90 by 2: 90 ÷ 2 = 45
Divide 45 by 3: 45 ÷ 3 = 15
Divide 15 by 3: 15 ÷ 3 = 5
So, the prime factors of 360 are 2, 2, 2, 3, and 5.
Now, let's express 360 as powers of its prime factors:
360 = 2^3 × 3^2 × 5
Therefore, 360 can be written as 2 raised to the power of 3, multiplied by 3 raised to the power of 2, multiplied by 5.