The expression you provided, $2 \times \frac{4}{3^2} \left(8m^2 \times \frac{4}{3} - \frac{4}{3}\right)$, seems to have some formatting issues that might lead to confusion. Let's clarify the expression step-by-step and simplify it.

Step 1: Understand the Expression

The expression appears to be:

$2 \times \frac{4}{3^2} \left(8m^2 \times \frac{4}{3} - \frac{4}{3}\right)$

Breaking it down:

1. $2 \times \frac{4}{3^2}$
2. Inside the parentheses: $8m^2 \times \frac{4}{3} - \frac{4}{3}$

Step 2: Simplify the Components

1. Simplify $\frac{4}{3^2}$: $\frac{4}{3^2} = \frac{4}{9}$

2. Calculate $2 \times \frac{4}{9}$: $2 \times \frac{4}{9} = \frac{8}{9}$

3. Simplify the expression inside the parentheses:

   • Multiply $8m^2 \times \frac{4}{3}$: $8m^2 \times \frac{4}{3} = \frac{32m^2}{3}$
   • Subtract $\frac{4}{3}$: $\frac{32m^2}{3} - \frac{4}{3} = \frac{32m^2 - 4}{3} = \frac{4(8m^2 - 1)}{3}$

Step 3: Combine and Simplify the Entire Expression

Now, combine the results from Step 2:

$\frac{8}{9} \times \frac{4(8m^2 - 1)}{3}$

This can be simplified as:

$\frac{8 \times 4(8m^2 - 1)}{9 \times 3} = \frac{32(8m^2 - 1)}{27}$

Final Answer

The simplified form of the expression is:

$\frac{32(8m^2 - 1)}{27}$

Would you like a more detailed breakdown or have any questions?

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Tip:

Always double-check the order of operations (PEMDAS/BODMAS) when simplifying complex expressions to avoid mistakes!