Let's break down the evaluation of each numerical expression step by step.
1. Expression 1: [tex]\( 5.6 \div 2^3 + (12.75 + 7.45) \)[/tex]
- Start by evaluating the exponent: [tex]\( 2^3 = 8 \)[/tex].
- Next, perform the division: [tex]\( 5.6 \div 8 = 0.7 \)[/tex].
- Inside the parentheses, add the numbers: [tex]\( 12.75 + 7.45 = 20.2 \)[/tex].
- Finally, add the results together: [tex]\( 0.7 + 20.2 = 20.9 \)[/tex].
Therefore, the value of [tex]\( 5.6 \div 2^3 + (12.75 + 7.45) \)[/tex] is 20.9.
2. Expression 2: [tex]\( 4^3 \times (0.6 + 3.6) \div 0.3 \)[/tex]
- Start by evaluating the exponent: [tex]\( 4^3 = 64 \)[/tex].
- Inside the parentheses, add the numbers: [tex]\( 0.6 + 3.6 = 4.2 \)[/tex].
- Next, perform the multiplication: [tex]\( 64 \times 4.2 = 268.8 \)[/tex].
- Finally, perform the division: [tex]\( 268.8 \div 0.3 = 896 \)[/tex].
Therefore, the value of [tex]\( 4^3 \times (0.6 + 3.6) \div 0.3 \)[/tex] is 896.
Matching the expressions with their values, we get:
- [tex]\( 5.6 \div 2^3 + (12.75 + 7.45) \)[/tex] matches with 20.9.
- [tex]\( 4^3 \times (0.6 + 3.6) \div 0.3 \)[/tex] matches with 896.
