Question

Which of the following shows a number as a product of prime numbers in exponential form? Choose all that apply. 5^2 * 7 * 13 7^2 * 24 3^2 * 13 4 * 5^3

Answer 1

A and C, because prime numbers are numbers that can be divided evenly only by 1 and itself. 2, 5, 7, 13 are prime numbers.

Answer 2

Answer:

$5^2\times7\times13$.

$3^2\times13$.

Step-by-step explanation:

Prime number: The number which have only two factors 1 and itself is called prime number .

A.$5^2\times7\times13$

The given number is the product of 5,5 ,7 and 13.

5 is a prime number because it has only two factors 1 and 5.

7 is a prime number because it has only  two factors 1 and 7.

13 is a prime number because it has only two factors 1 and 13.

Hence, the number shows as a product of prime numbers in exponential form.

B.$7^2\times24$

The number is the product of $7^2 and 24$.

7 is a prime number  because it has only two factors 1 and itself.

24 is not prime number because it has more than two factors.

Hence, the number does not shows as product of prime numbers in exponential form.

C.$3^2\times13$

The number is the product of $3^2 and 13$

3 is a prime number because it has two factors 1 and 3.

13 is  a prime number because it has two factors 1 and 13.

Hence, the number shows as the product of prime number in exponential form.

D.$4\times5^3$

The number is the product of 4 and $5^3$

5 is a prime number because it has two factors 1 and 5.

4 is not a prime number because it has more than two factors.

Hence, the number does not shows as the product of prime numbers in exponential form.