R. D. Sharma Solutions for Chapter: Real Numbers, Exercise 3: EXERCISE 1.3

The prime factorisation of $420$ can be written as $2^A\times 3^B\times 5^C\times 7^D$. Find the value of $A+B+C+D$.

$468$ can be written as a product of prime numbers as $2^2\times A^2\times B$. Find the value of $B-A$.

Prime factorisation of $945$ can be written as $3^A\times 5\times B$. Find the value of $B-A$. 

The prime factorisation of $7325$, can be expressed as $A^2\times B$, find the value of $B-A$.

If the prime factorisation of $20570$ can be written as $2\times 5\times A^2\times B$, then find the value of $A+B$.

The prime factorization of the number $58500$ can be written as $2^2\times A^2\times 5^3\times B$, find the value of $A+B$.

The prime factorisation of the number $45470971$ can be written as $7^2\times A^2\times B^2\times 19$, then find the value of $B-A$.

Explain why $3\times 5\times 7+7$ is a composite number.