-   Given expression = (0.2 x 0.2 + 0.01) = 0.04 + 0.01 = 0.05 = 5 (0.1 x 0.1 + 0.02) 0.01 + 0.02 0.03 3

To solve the expression (0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)-1, we can use the order of operations (PEMDAS) and simplify step by step:

Step 1: Simplify the terms inside the parentheses:

(0.2 x 0.2 + 0.01) = 0.045

(0.1 x 0.1 + 0.02) = 0.012

Step 2: Raise the expression inside the parentheses to the power of -1 (or take the reciprocal):

(0.045) (0.012)-1 = (0.045) (83.33...) = 3.75

Step 3: Simplify the final result by dividing by 2:

3.75 / 2 = 1.875

Therefore, the answer is not one of the given options. However, we can check our calculations and see that we made a mistake in step 2. We need to raise the entire expression to the power of -1, not just the second term inside the parentheses:

(0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)-1 = (0.045) (0.012)-1

Using the formula a-n = 1/an, we can rewrite the expression as:

(0.045) / (0.012)

Simplifying, we get:

(0.045) / (0.012) = 3.75

Finally, we divide by 2 to get the correct answer:

3.75 / 2 = 1.875

Therefore, the correct option is not given. However, we can simplify the expression further:

(0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)-1

= (0.04 + 0.01) (0.01 + 0.02)-1

= 0.05 (0.03)-1

= 5/3

Therefore, the correct answer is option A, 5/3.

If you think the solution is wrong then please provide your own solution below in the comments section .