Question

(- 3/4) ^ 4 - (1/16) ^ 2 + 17

Answer 1

To calculate the expression (-3/4)^4 - (1/16)^2 + 17, you can follow these steps:

1. Calculate (-3/4)^4: (-3/4)^4 = (-3/4) * (-3/4) * (-3/4) * (-3/4) = 81/256

2. Calculate (1/16)^2: (1/16)^2 = (1/16) * (1/16) = 1/256

3. Now, subtract the results from step 1 and step 2 and add 17: 81/256 - 1/256 + 17

4. Combine the fractions with the same denominator: (81/256 - 1/256) + 17

5. Subtract the fractions: 80/256 + 17

6. Simplify the fraction: 80/256 reduces to 5/16

7. Add 17 to the simplified fraction: 5/16 + 17

To add a fraction to a whole number, you need to have the same denominator, so we can rewrite 17 as 272/16 (since 17 = 16 + 1):

5/16 + 272/16 = (5 + 272)/16 = 277/16

So, the final result is 277/16.