Question

Express each of the following as a product of prime factors only in exponential form.
$270$

Answer 1

Hint: First solve this in prime factorization method and then convert into prime factors of exponential form.

Starting with the first prime number we can write $270$as
$270=2\times 135$
Then converting $135$ into the factors of next prime number $3$we have
$270=2\times 3\times 45$
Again converting $45$into the prime factors of $3$ we have
$270=2\times 3\times 3\times 15$
Now at last converting $15$into the prime factors of $3$and $5$ we have
$270=2\times 3\times 3\times 3\times 5$

Finally, converting them into exponential form we have
$$270=2^1\times 3^3\times 5^1$$
Thus, the product of prime factors in the exponential form of $$270$$is $$2^1\times 3^3\times 5^1$$

Note: In this type of problems first write prime factors of lower prime numbers and then to higher
prime numbers.