QuestionWhich option shows the prime factorization of 200 in exponential form? $8 \cdot 25$ $2^{3} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ $2 \cdot 10^{2}$

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of200. . The prime factorization should be in exponential notation.
3. The prime factorization of a number is the expression of the number as a product of its prime factors.

STEP 2

Let's start by finding the prime factors of200. We can do this by dividing200 by the smallest prime number, which is2, and continue dividing the quotient by2 until we get a quotient that is not divisible by2.
$200 /2 =100$ $100 /2 =50$ $50 /2 =25$

STEP 3

Now, we can see that25 is not divisible by2, so we move on to the next prime number, which is3. But25 is not divisible by3, so we move on to the next prime number, which is5. We continue dividing by5 until we get a quotient that is not divisible by5.
$25 /5 =5$ $5 /5 =1$

STEP 4

Now that we have all the prime factors of200, we can write them down.
$2,2,2,,$

STEP 5

To express the prime factorization in exponential notation, we count how many times each prime number appears in the factorization.
$2^{3},5^{2}$

STEP 6

Finally, we write the prime factorization of200 in exponential notation as a product of the prime factors.
$200 =2^{3} \cdot5^{2}$ So, the correct answer is $2^{3} \cdot5^{2}$ .

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QuestionWhich option shows the prime factorization of 200 in exponential form? $8 \cdot 25$ $2^{3} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ $2 \cdot 10^{2}$

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of200. . The prime factorization should be in exponential notation.
3. The prime factorization of a number is the expression of the number as a product of its prime factors.

STEP 2

Let's start by finding the prime factors of200. We can do this by dividing200 by the smallest prime number, which is2, and continue dividing the quotient by2 until we get a quotient that is not divisible by2.
$200 /2 =100$ $100 /2 =50$ $50 /2 =25$

STEP 3

Now, we can see that25 is not divisible by2, so we move on to the next prime number, which is3. But25 is not divisible by3, so we move on to the next prime number, which is5. We continue dividing by5 until we get a quotient that is not divisible by5.
$25 /5 =5$ $5 /5 =1$

STEP 4

Now that we have all the prime factors of200, we can write them down.
$2,2,2,,$

STEP 5

To express the prime factorization in exponential notation, we count how many times each prime number appears in the factorization.
$2^{3},5^{2}$

STEP 6

Finally, we write the prime factorization of200 in exponential notation as a product of the prime factors.
$200 =2^{3} \cdot5^{2}$ So, the correct answer is $2^{3} \cdot5^{2}$ .

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QuestionWhich option shows the prime factorization of 200 in exponential form? 8⋅258 \cdot 258⋅25 23⋅522^{3} \cdot 5^{2}23⋅52 22⋅522^{2} \cdot 5^{2}22⋅52 2⋅1022 \cdot 10^{2}2⋅102

Studdy Solution

STEP 1

Assumptions1. We are asked to find the prime factorization of200. . The prime factorization should be in exponential notation.3. The prime factorization of a number is the expression of the number as a product of its prime factors.

STEP 2

Let's start by finding the prime factors of200. We can do this by dividing200 by the smallest prime number, which is2, and continue dividing the quotient by2 until we get a quotient that is not divisible by2.200/2=100200 /2 =100200/2=100100/2=50100 /2 =50100/2=5050/2=2550 /2 =2550/2=25

STEP 3

Now, we can see that25 is not divisible by2, so we move on to the next prime number, which is3. But25 is not divisible by3, so we move on to the next prime number, which is5. We continue dividing by5 until we get a quotient that is not divisible by5.25/5=525 /5 =525/5=55/5=15 /5 =15/5=1

STEP 4

Now that we have all the prime factors of200, we can write them down.2,2,2,,2,2,2,,2,2,2,,

STEP 5

To express the prime factorization in exponential notation, we count how many times each prime number appears in the factorization.23,522^{3},5^{2}23,52

STEP 6

Finally, we write the prime factorization of200 in exponential notation as a product of the prime factors.200=23⋅52200 =2^{3} \cdot5^{2}200=23⋅52So, the correct answer is 23⋅522^{3} \cdot5^{2}23⋅52.

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QuestionWhich option shows the prime factorization of 200 in exponential form? $8 \cdot 25$ $2^{3} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ $2 \cdot 10^{2}$

Assumptions1. We are asked to find the prime factorization of200. . The prime factorization should be in exponential notation.
3. The prime factorization of a number is the expression of the number as a product of its prime factors.

Let's start by finding the prime factors of200. We can do this by dividing200 by the smallest prime number, which is2, and continue dividing the quotient by2 until we get a quotient that is not divisible by2.
$200 /2 =100$ $100 /2 =50$ $50 /2 =25$

Now, we can see that25 is not divisible by2, so we move on to the next prime number, which is3. But25 is not divisible by3, so we move on to the next prime number, which is5. We continue dividing by5 until we get a quotient that is not divisible by5.
$25 /5 =5$ $5 /5 =1$

Now that we have all the prime factors of200, we can write them down.
$2,2,2,,$

To express the prime factorization in exponential notation, we count how many times each prime number appears in the factorization.
$2^{3},5^{2}$

Finally, we write the prime factorization of200 in exponential notation as a product of the prime factors.
$200 =2^{3} \cdot5^{2}$ So, the correct answer is $2^{3} \cdot5^{2}$ .