[Omprakash]

To find the values of a and b when the sum of a and b is 60 and their ratio is 3:2, we can set up a system of equations and solve for the variables.

Let’s denote a as 3x and b as 2x, where x is a common factor.

Given: a + b = 60 (Equation 1) a:b = 3:2 (Equation 2)

Substituting the values of a and b in Equation 1: 3x + 2x = 60

Combining like terms: 5x = 60

Dividing both sides by 5: x = 12

Now, substitute the value of x back into the expressions for a and b: a = 3x = 3 * 12 = 36 b = 2x = 2 * 12 = 24

Therefore, the values of a and b are: a = 36 b = 24

[Omprakash]

Step 1: Evaluate the numbers with exponents. 3² = 3 × 3 = 9 2⁴ = 2 × 2 × 2 × 2 = 16 6⁴ = 6 × 6 × 6 × 6 = 1,296 3⁰ = 1 (Any number raised to the power of zero is always 1.)

Step 2: Substitute the values back into the expression. (9 × 16) ÷ (1,296 × 1)

Step 3: Simplify further. 9 × 16 = 144 1,296 × 1 = 1,296

Step 4: Final answer. 144 ÷ 1,296 = 0.111111…

So, the simplified form of (3² × 2⁴) ÷ (6⁴ × 3⁰) is approximately 0.111111…