Final answer:
The expression 'The difference between three-fourths of eight and seven to the second power' translates to 6 - 49 and simplifies to –43.
Step-by-step explanation:
The student's question asks to translate and simplify the following expression: 'The difference between three-fourths of eight and seven to the second power.'
Firstly, let's translate this into a mathematical expression. Three-fourths of eight is ⅓ × 8, which equates to 6. Seven to the second power refers to 7², which is 49. The difference between the two expressions means we will subtract the second from the first, resulting in the following expression: 6 - 49.
Now to simplify the expression:
- Calculate three-fourths of eight: ⅓ × 8 = 2×4 = 6.
- Compute seven squared: 7² = 7×7 = 49.
- Subtract seven squared from three-fourths of eight: 6 - 49 = -43.
The simplified expression is -43.