Write 100 as a product of its primes. Simplify the fraction 84/96. Write 5/8 as a decimal fraction correct to two decimal places. Calculate 30% of 500 kg.

Divide 100 by the smallest prime number, 2.
$100 \div 2 = 50$
Divide 50 by 2.
$50 \div 2 = 25$
Divide 25 by the next smallest prime number, 5.
$25 \div 5 = 5$
Divide 5 by 5.
$5 \div 5 = 1$
The prime factors are 2, 2, 5, 5.

The product of its primes is $\boxed{\mathbf{2^2 \times 5^2}}$.

2. Simplify the fraction $\frac{84}{96}$.

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The greatest common divisor is 12.

The simplified fraction is $\boxed{\mathbf{\frac{7}{8}}}$.

3. Write $\frac{5}{8}$ as a decimal fraction correct to two decimal places.

Divide 5 by 8.

The third decimal place is 5, so round up the second decimal place.

The decimal fraction correct to two decimal places is $\boxed{\mathbf{0.63}}$.

4. Calculate 30% of 500 kg.

30% of 500 kg is $\boxed{\mathbf{150 \text{ kg}}}$.