Express, in index notation, 150 as a product of its prime factors, using a factor tree.
To express 150 as a product of its prime factors using a factor tree, we start by dividing 150 by its smallest prime factor, which is 2.
150 ÷ 2 = 75
Next, we divide 75 by its smallest prime factor, which is 3.
75 ÷ 3 = 25
Now, 25 is already a square number, so we stop here because we cannot divide it any further. Therefore, the prime factorization of 150 is:
150 = 2 * 3 * 5 * 5, or in index notation:
150 = 2^1 * 3^1 * 5^2
To express 150 as a product of its prime factors using a factor tree and index notation, we can start by finding the prime factors of 150.
First, let's divide 150 by 2, since 2 is the smallest prime number that can divide 150 evenly. We get:
150 ÷ 2 = 75
Now, let's divide 75 by 3, another prime number:
75 ÷ 3 = 25
Next, let's divide 25 by 5:
25 ÷ 5 = 5
Since 5 is a prime number, we have completed the factor tree. The prime factors of 150 are 2, 3, 5.
Using index notation, we can write 150 as a product of its prime factors:
150 = 2^1 × 3^1 × 5^2
So, 150 can be expressed as the product of its prime factors using index notation as 2 raised to the power of 1, multiplied by 3 raised to the power of 1, multiplied by 5 raised to the power of 2.