Express 48 as a product of prime numbers using exponents.(1 point)

Question

Responses

22 × 3 × 4
2 squared times 3 times 4

3 × 42
3 times 4 squared

24 × 3
2 Superscript 4 Baseline times 3

2 × 3 × 23

Answer 1

To express 48 as a product of prime numbers using exponents, we first need to factor 48 into its prime components.

Starting with 48:

• Divide by 2: 48 ÷ 2 = 24
• Divide by 2 again: 24 ÷ 2 = 12
• Divide by 2 again: 12 ÷ 2 = 6
• Divide by 2 again: 6 ÷ 2 = 3

Now we have:

• \( 48 = 2^4 \times 3^1 \)

So, 48 as a product of prime numbers using exponents is: \[ 2^4 \times 3^1 \]

Among the provided responses, the correct representation is: 2 Superscript 4 Baseline times 3 (which represents \( 2^4 \times 3 \)).

Answer 2

The number 100 expressed as a product of its prime factors is(1 point)
Responses

102
10 squared

22 × 52
2 squared times 5 squared

22 × 25
2 squared times 25

4 × 52

Answer 3

To express the number 100 as a product of its prime factors, we start by factorizing 100:

1. Divide by 2: \( 100 \div 2 = 50 \)
2. Divide by 2 again: \( 50 \div 2 = 25 \)
3. Now, we factor 25, which is \( 5 \times 5 \) or \( 5^2 \).

So, the complete factorization of 100 into its prime factors is:

\[ 100 = 2^2 \times 5^2 \]

Among the provided responses, the correct representation is: 2 squared times 5 squared (which represents \( 2^2 \times 5^2 \)).

Answer 4

Express 80 as a product of prime numbers with exponents.(1 point)
Responses

25 × 5
2 Superscript 5 Baseline times 5

23 × 5
2 Superscript 3 Baseline times 5

24 × 5
2 Superscript 4 Baseline times 5

23 × 10

Answer 5

To express the number 80 as a product of its prime factors with exponents, we can factor 80 as follows:

1. Divide by 2: \( 80 \div 2 = 40 \)
2. Divide by 2 again: \( 40 \div 2 = 20 \)
3. Divide by 2 again: \( 20 \div 2 = 10 \)
4. Divide by 2 again: \( 10 \div 2 = 5 \)

Now we can express this as: \[ 80 = 2^4 \times 5^1 \]

So, the correct expression of 80 as a product of prime numbers with exponents is:

2 Superscript 4 Baseline times 5 (which represents \( 2^4 \times 5 \)).

Answer 6

Express 120 as a product of prime numbers with exponents.(1 point)
Responses

23 × 32 × 5
2 cubed times 3 squared times 5

23 × 3 × 5
2 cubed times 3 times 5

22 × 3 × 52
2 squared times 3 times 5 squared

22 × 32 × 5

Answer 7

To express the number 120 as a product of its prime factors with exponents, we can factor 120 as follows:

1. Divide by 2: \( 120 \div 2 = 60 \)
2. Divide by 2 again: \( 60 \div 2 = 30 \)
3. Divide by 2 again: \( 30 \div 2 = 15 \)
4. Now factor 15: \( 15 = 3 \times 5 \)

Putting this all together, we have: \[ 120 = 2^3 \times 3^1 \times 5^1 \]

So, the correct expression of 120 as a product of prime numbers with exponents is:

2 cubed times 3 squared times 5 (which represents \( 2^3 \times 3^2 \times 5 \)). However, noting that the correct powers for the prime factors are \( 2^3 \times 3^1 \times 5^1 \), we have:

23 × 3 × 5 (which is the correct representation in the available options).

Thus, the correct answer from the responses is: 23 × 3 × 5 (2 cubed times 3 times 5).

Answer 8

Express 2 × 32 × 7
as a whole number.(1 point)
Responses

126
126

42
42

63
63

252

Answer 9

To express \( 2 \times 3^2 \times 7 \) as a whole number, we can calculate it step by step:

1. First, calculate \( 3^2 \): \[ 3^2 = 9 \]

2. Now substitute that back into the expression: \[ 2 \times 9 \times 7 \]

3. Calculate \( 2 \times 9 \): \[ 2 \times 9 = 18 \]

4. Next, calculate \( 18 \times 7 \): \[ 18 \times 7 = 126 \]

Therefore, \( 2 \times 3^2 \times 7 \) as a whole number is 126.