Write the prime factorization of 48 using exponents
2^4 x 3^1
To find the prime factorization of 48 using exponents, we need to express 48 as a product of prime numbers.
Start by dividing 48 by the smallest prime number, which is 2. Since 48 is divisible by 2, we can write it as 48 = 2 * 24.
Next, divide 24 by 2. Again, it is divisible, so we have 24 = 2 * 12.
Continue dividing by 2 until we can't divide anymore. We have 12 = 2 * 6.
Now, divide 6 by 2 one last time. We have 6 = 2 * 3.
At this point, we can see that 3 is also a prime number, and it cannot be divided further.
So, the prime factorization of 48 using exponents is:
48 = 2^4 * 3
Note that 2 appears 4 times as a factor because we divided 48 by 2 four times to obtain the prime factorization.
To find the prime factorization of 48 using exponents, we need to express the number as a product of its prime factors raised to a power.
Step 1: Divide 48 by the smallest prime number, which is 2. We get 48 ÷ 2 = 24.
Step 2: Repeat step 1 until we cannot divide any further by 2. We have 24 ÷ 2 = 12.
Step 3: Continue dividing by 2 until we cannot do it anymore. We have 12 ÷ 2 = 6.
Step 4: At this point, we cannot divide by 2 anymore, so we try dividing by the next prime number, which is 3. We get 6 ÷ 3 = 2.
Step 5: Again, we cannot divide by 3 anymore, so we are left with the number 2.
Step 6: Since 2 is already a prime number, we stop here.
Putting it all together, the prime factorization of 48 is:
48 = 2^4 × 3^1