Question

Express $1000$ as product of powers of their prime factors.

Answer 1

Let's learn what are prime factors: A factor that is a prime number is a prime factor. Prime factors are the prime numbers that can be multiplied to give the original number, for example, Thr prime factors of $15$ are $3$ and $5$(because $3\times 5=15$, and $3$ and $5$are prime numbers,i.e., those which have only two factors: $1$ and themselves).

So, now we will find the factors as the prime numbers of $1000$ .

Now,$1000=2\times 2\times 2\times 5\times 5\times 5=2^3\times 5^3$($2$ and $5$ are the prime factors of the number)

Hence, the product of powers of the prime factors of $1000$ can be expressed as $2^3\times 5^3$.