Simplifying the Expression:

To simplify the given expression, we will follow the order of operations (PEMDAS) and evaluate each part step by step.

Step 1: Simplify Exponents
We start by simplifying the exponents in the expression. Let's break it down:

8^2/3:
To simplify an exponent with a fractional power, we need to take the numerator as the exponent and the denominator as the root. So, 8^2/3 can be written as the cube root of 8 squared: ∛(8^2). Calculating this, we have ∛64 = 4.

(1/144)^-1/2:
The negative exponent indicates that we need to take the reciprocal of the base. So, (1/144)^-1/2 is equivalent to 1 / (1/144)^(1/2). Simplifying further, we have 1 / (1/12) = 12.

Step 2: Simplify Multiplication and Division
Now, let's simplify the multiplication and division parts of the expression:

√9 * 10^0:
√9 is equal to the square root of 9, which is 3. 10^0 is equal to 1 since any number raised to the power of 0 is always 1. Multiplying these values, we get 3 * 1 = 3.

Step 3: Simplify Addition and Subtraction
Now that we have simplified the exponents and multiplication/division, we can perform the final addition/subtraction:

4 - 3:
Subtracting 3 from 4 gives us the final result of 1.

Final Answer:
Therefore, the simplified expression is equal to 1.

Summary:
1. Simplify the exponents in the expression:
- 8^2/3 = ∛(8^2) = ∛64 = 4
- (1/144)^-1/2 = 1 / (1/144)^(1/2) = 1 / (1/12) = 12
2. Simplify the multiplication and division:
- √9 * 10^0 = 3 * 1 = 3
3. Simplify the addition and subtraction:
- 4 - 3 = 1
4. Therefore, the simplified expression is equal to 1.