Answer:
135 can be expressed as a product of powers of its prime factors as 3 cubed (3^3) times 5.
Explanation:
To express the number 135 as a product of its prime factors, you need to factor it into prime numbers. Here's how you can do it:
1. Start by dividing 135 by the smallest prime number, which is 2. But 135 is an odd number and not divisible by 2.
2. Move on to the next smallest prime number, which is 3. Divide 135 by 3:
135 ÷ 3 = 45
3. Now, we continue factoring 45. Divide 45 by 3 again:
45 ÷ 3 = 15
4. Continue factoring 15. Divide 15 by 3 once more:
15 ÷ 3 = 5
5. Now, we have reached a prime number, 5, which is also a factor of 5.
So, the prime factorization of 135 is:
135 = 3 × 3 × 3 × 5
You can express this as a product of powers of its prime factors as follows:
135 = (3^3) × 5
So, 135 can be expressed as a product of powers of its prime factors as 3 cubed (3^3) times 5.