Question

[4 - (2/3) ^ 2] ^ - 1 * (1/2) ^ -2 =

Answer 1

$(4 - \frac{4}{9} ) {}^{ - 1} \times {2}^{2} = ( \frac{36}{9} - \frac{4}{9} ) {}^{ - 1} \times 4 = ( \frac{32}{9} ) {}^{ - 1} \times 4 = \frac{9}{32} \times 4 = \frac{9}{8 \times 4} = \frac{9}{8} = 1 \frac{1}{8}$

Answer 2

To solve this expression step by step, follow the order of operations (PEMDAS/BODMAS):

1. First, evaluate the exponents within parentheses:

   (2/3)^2 = 4/9 (1/2)^(-2) = 4

2. Substitute these values back into the original expression:

   [4 - (4/9)]^(-1) * 4

3. Subtract 4/9 from 4:

   (36/9 - 4/9)^(-1) * 4

4. Combine like terms within the brackets:

   (32/9)^(-1) * 4

5. To evaluate a negative exponent, take the reciprocal:

   (9/32) * 4

6. Multiply the fractions:

   (9/32) * 4 = 36/32 = 9/8

So, the final result is 9/8.