Answer :
Let's evaluate each expression step-by-step, using the order of operations (PEMDAS/BODMAS).
### Expression 1:
[tex]\[ (2 - 4)^2 - 7 \][/tex]
1. First, subtract inside the parentheses:
[tex]\[ 2 - 4 = -2 \][/tex]
2. Then, square the result:
[tex]\[ (-2)^2 = 4 \][/tex]
3. Finally, subtract 7:
[tex]\[ 4 - 7 = -3 \][/tex]
So,
[tex]\[ (2 - 4)^2 - 7 = -3 \][/tex]
### Expression 2:
[tex]\[ (-7)^2 - 7(-7) - 9 \cdot 9^2 + 5 \][/tex]
1. First, evaluate the exponentiation:
[tex]\[ (-7)^2 = 49 \][/tex]
[tex]\[ 9^2 = 81 \][/tex]
2. Then, multiply:
[tex]\[ 7(-7) = -49 \][/tex]
[tex]\[ 9 \cdot 81 = 729 \][/tex]
3. Substitute these values back into the expression:
[tex]\[ 49 - (-49) - 729 + 5 \][/tex]
4. Simplify within the subtractions and additions:
- Change the minus a negative to a plus:
[tex]\[ 49 + 49 - 729 + 5 \][/tex]
5. Finally, add and subtract in order from left to right:
[tex]\[ 98 - 729 + 5 = -631 + 5 = -626 \][/tex]
So,
[tex]\[ (-7)^2 - 7(-7) - 9 \cdot 9^2 + 5 = -626 \][/tex]
### Expression 3:
[tex]\[ 7 - 6(9^2 - 5) - (-2) \][/tex]
1. First, evaluate inside the parentheses:
[tex]\[ 9^2 = 81 \][/tex]
[tex]\[ 81 - 5 = 76 \][/tex]
2. Substitute back into the expression:
[tex]\[ 7 - 6(76) - (-2) \][/tex]
3. Then, multiply:
[tex]\[ 6 \cdot 76 = 456 \][/tex]
4. Substitute and simplify:
[tex]\[ 7 - 456 + 2 \][/tex]
5. Finally, perform the additions and subtractions in order:
[tex]\[ 7 - 456 + 2 = -449 + 2 = -447 \][/tex]
So,
[tex]\[ 7 - 6(9^2 - 5) - (-2) = -447 \][/tex]
### Expression 4:
[tex]\[ 5(-3)^2 + 63 \div (-9) \][/tex]
1. First, evaluate the exponentiation:
[tex]\[ (-3)^2 = 9 \][/tex]
2. Substitute back into the expression and multiply:
[tex]\[ 5 \cdot 9 + 63 \div (-9) \][/tex]
3. Then, perform the division:
[tex]\[ 63 \div (-9) = -7 \][/tex]
4. Finally, add the results:
[tex]\[ 45 - 7 = 38 \][/tex]
So,
[tex]\[ 5(-3)^2 + 63 \div (-9) = 38 \][/tex]
### Expression 5:
[tex]\[ (-5) - (-4)(2^3 - (-3)) \][/tex]
1. First, evaluate the exponentiation:
[tex]\[ 2^3 = 8 \][/tex]
2. Then, evaluate inside the inner parentheses:
[tex]\[ 8 - (-3) = 8 + 3 = 11 \][/tex]
3. Substitute back into the expression and multiply:
[tex]\[ (-5) - (-4)(11) \][/tex]
[tex]\[ (-4) \cdot 11 = -44 \][/tex]
4. Finally, perform the subtraction:
[tex]\[ (-5) + 44 = 39 \][/tex]
So,
[tex]\[ (-5) - (-4)(2^3 - (-3)) = 39 \][/tex]
The evaluated results are:
[tex]\[ \begin{array}{c|c} (2-4)^2-7 = -3 \\ (-7)^2 - 7(-7) - 9 \cdot 9^2 + 5 = -626 \\ 7 - 6(9^2 - 5) - (-2) = -447 & 5(-3)^2 + 63 \div (-9) = 38 \\ & (-5) - (-4)(2^3 - (-3)) = 39 \end{array} \][/tex]
### Expression 1:
[tex]\[ (2 - 4)^2 - 7 \][/tex]
1. First, subtract inside the parentheses:
[tex]\[ 2 - 4 = -2 \][/tex]
2. Then, square the result:
[tex]\[ (-2)^2 = 4 \][/tex]
3. Finally, subtract 7:
[tex]\[ 4 - 7 = -3 \][/tex]
So,
[tex]\[ (2 - 4)^2 - 7 = -3 \][/tex]
### Expression 2:
[tex]\[ (-7)^2 - 7(-7) - 9 \cdot 9^2 + 5 \][/tex]
1. First, evaluate the exponentiation:
[tex]\[ (-7)^2 = 49 \][/tex]
[tex]\[ 9^2 = 81 \][/tex]
2. Then, multiply:
[tex]\[ 7(-7) = -49 \][/tex]
[tex]\[ 9 \cdot 81 = 729 \][/tex]
3. Substitute these values back into the expression:
[tex]\[ 49 - (-49) - 729 + 5 \][/tex]
4. Simplify within the subtractions and additions:
- Change the minus a negative to a plus:
[tex]\[ 49 + 49 - 729 + 5 \][/tex]
5. Finally, add and subtract in order from left to right:
[tex]\[ 98 - 729 + 5 = -631 + 5 = -626 \][/tex]
So,
[tex]\[ (-7)^2 - 7(-7) - 9 \cdot 9^2 + 5 = -626 \][/tex]
### Expression 3:
[tex]\[ 7 - 6(9^2 - 5) - (-2) \][/tex]
1. First, evaluate inside the parentheses:
[tex]\[ 9^2 = 81 \][/tex]
[tex]\[ 81 - 5 = 76 \][/tex]
2. Substitute back into the expression:
[tex]\[ 7 - 6(76) - (-2) \][/tex]
3. Then, multiply:
[tex]\[ 6 \cdot 76 = 456 \][/tex]
4. Substitute and simplify:
[tex]\[ 7 - 456 + 2 \][/tex]
5. Finally, perform the additions and subtractions in order:
[tex]\[ 7 - 456 + 2 = -449 + 2 = -447 \][/tex]
So,
[tex]\[ 7 - 6(9^2 - 5) - (-2) = -447 \][/tex]
### Expression 4:
[tex]\[ 5(-3)^2 + 63 \div (-9) \][/tex]
1. First, evaluate the exponentiation:
[tex]\[ (-3)^2 = 9 \][/tex]
2. Substitute back into the expression and multiply:
[tex]\[ 5 \cdot 9 + 63 \div (-9) \][/tex]
3. Then, perform the division:
[tex]\[ 63 \div (-9) = -7 \][/tex]
4. Finally, add the results:
[tex]\[ 45 - 7 = 38 \][/tex]
So,
[tex]\[ 5(-3)^2 + 63 \div (-9) = 38 \][/tex]
### Expression 5:
[tex]\[ (-5) - (-4)(2^3 - (-3)) \][/tex]
1. First, evaluate the exponentiation:
[tex]\[ 2^3 = 8 \][/tex]
2. Then, evaluate inside the inner parentheses:
[tex]\[ 8 - (-3) = 8 + 3 = 11 \][/tex]
3. Substitute back into the expression and multiply:
[tex]\[ (-5) - (-4)(11) \][/tex]
[tex]\[ (-4) \cdot 11 = -44 \][/tex]
4. Finally, perform the subtraction:
[tex]\[ (-5) + 44 = 39 \][/tex]
So,
[tex]\[ (-5) - (-4)(2^3 - (-3)) = 39 \][/tex]
The evaluated results are:
[tex]\[ \begin{array}{c|c} (2-4)^2-7 = -3 \\ (-7)^2 - 7(-7) - 9 \cdot 9^2 + 5 = -626 \\ 7 - 6(9^2 - 5) - (-2) = -447 & 5(-3)^2 + 63 \div (-9) = 38 \\ & (-5) - (-4)(2^3 - (-3)) = 39 \end{array} \][/tex]
