Product of their prime factors

Whats the difference between expressing a number as the product of their prime factors and expressing a number as the product of powers or their prime factors.

Example Express the number 60 as a the product of its prime factors and
Express the number 24 as the prouct of POWERS of its prime factors


Does it mean the same thing or...

two cakes made of same materials but design of two cake is different.
this is the answer for your question

60 = 2 x 2 x 3 x 5 ------ product of prime factors
60 = 2² x 3 x 5 -----------product of powers of prime factors

24 = 2 x 2 x 2 x 3 ------ product of prime factors
24 = 2³ x 3 -----------product of powers of prime factors

Expressing as a product means write the number in terms of primes multiplied together.
24=8X3=2X2X2X3which is the product of its prime factors.
It can also be written as 2^3X3 which is the product of powers of the factors.
Note that 3=3^1.
I would accept that 2^3 X3 is the product of prime factors.

It means the same thing, with a little difference.

If it asks the PRIME FACTORS, not the PRODUCT, then the case is different, but if it asks the product the case is the same.

Take 12 for instance.

Product of its prime factors: 2.2.3
Product of the powers of its prime factors: 2^2.3^1

Note that 2^2 = 2.2 and 3^1 = 3.

60 = 12 X 5 = 3 X 4 X 5 = 2 X 2 X 3 X 5
24 = 8 X 3 = 2^3 X 3