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Sagot :
Certainly! Let's go through each expression step-by-step to find their values.
1. Evaluate [tex]\((2-4)^2 - 7\)[/tex]
- Perform the subtraction inside the parentheses: [tex]\(2-4 = -2\)[/tex].
- Square the result: [tex]\((-2)^2 = 4\)[/tex].
- Subtract 7: [tex]\(4 - 7 = -3\)[/tex].
Result: [tex]\((-3\)[/tex])
2. Evaluate [tex]\(6 \cdot 9^2 + 5\)[/tex]
- Calculate the exponent: [tex]\(9^2 = 81\)[/tex].
- Multiply by 6: [tex]\(6 \cdot 81 = 486\)[/tex].
- Add 5: [tex]\(486 + 5 = 491\)[/tex].
Result: [tex]\(491\)[/tex]
3. Evaluate [tex]\((-7)^2 - 7(-7) - 9\)[/tex]
- Square the negative number: [tex]\((-7)^2 = 49\)[/tex].
- Multiply [tex]\(-7\)[/tex] by [tex]\(-7\)[/tex]: [tex]\( -7 \cdot (-7) = 49\)[/tex].
- Combine the terms: [tex]\(49 + 49 - 9 = 89\)[/tex].
Result: [tex]\(89\)[/tex]
4. Evaluate [tex]\(5 \cdot (-3)^2 + 63 \div (-9)\)[/tex]
- Square the number: [tex]\((-3)^2 = 9\)[/tex].
- Multiply by 5: [tex]\(5 \cdot 9 = 45\)[/tex].
- Divide 63 by -9: [tex]\(63 \div (-9) = -7\)[/tex].
- Combine the terms: [tex]\(45 + (-7) = 38.0\)[/tex].
Result: [tex]\(38.0\)[/tex]
5. Evaluate [tex]\(7 - 6 \cdot (9^2 - 5) - (-2)\)[/tex]
- Calculate the exponent: [tex]\(9^2 = 81\)[/tex].
- Subtract inside the parentheses: [tex]\(81 - 5 = 76\)[/tex].
- Multiply by -6: [tex]\( -6 \cdot 76 = -456\)[/tex].
- Combine the terms: [tex]\(7 - 456 + 2 = -447\)[/tex].
Result: [tex]\(-447\)[/tex]
6. Evaluate [tex]\((-5) - (-4) \cdot (2^3 - (-3))\)[/tex]
- Calculate the exponent: [tex]\(2^3 = 8\)[/tex].
- Add inside the parentheses: [tex]\(8 + 3 = 11\)[/tex].
- Multiply by -4: [tex]\( -4 \cdot 11 = -44\)[/tex].
- Combine the terms: [tex]\(-5 + 44 = 39\)[/tex].
Result: [tex]\(39\)[/tex]
Thus, the computed values for all expressions are summarized as follows:
[tex]\[ \begin{array}{||r|r|} \hline \multicolumn{2}{|c|}{ Order of Operations: Add, Subtract, Multiply, Divide, Parentheses and Exponents } \\ \hline \hline Evaluate each of the following. \\ \hline(2-4)^2-7 = -3 \ & 6 \cdot 9^2+5 = 491 \\ \hline (-7)^2-7(-7)-9 = 89 \ & 5(-3)^2+63 \div (-9) = 38.0 \\ \hline 7-6(9^2-5)-(-2) = -447 \ & (-5)-(-4)(2^3-(-3)) = 39 \\ \hline \end{array} \][/tex]
1. Evaluate [tex]\((2-4)^2 - 7\)[/tex]
- Perform the subtraction inside the parentheses: [tex]\(2-4 = -2\)[/tex].
- Square the result: [tex]\((-2)^2 = 4\)[/tex].
- Subtract 7: [tex]\(4 - 7 = -3\)[/tex].
Result: [tex]\((-3\)[/tex])
2. Evaluate [tex]\(6 \cdot 9^2 + 5\)[/tex]
- Calculate the exponent: [tex]\(9^2 = 81\)[/tex].
- Multiply by 6: [tex]\(6 \cdot 81 = 486\)[/tex].
- Add 5: [tex]\(486 + 5 = 491\)[/tex].
Result: [tex]\(491\)[/tex]
3. Evaluate [tex]\((-7)^2 - 7(-7) - 9\)[/tex]
- Square the negative number: [tex]\((-7)^2 = 49\)[/tex].
- Multiply [tex]\(-7\)[/tex] by [tex]\(-7\)[/tex]: [tex]\( -7 \cdot (-7) = 49\)[/tex].
- Combine the terms: [tex]\(49 + 49 - 9 = 89\)[/tex].
Result: [tex]\(89\)[/tex]
4. Evaluate [tex]\(5 \cdot (-3)^2 + 63 \div (-9)\)[/tex]
- Square the number: [tex]\((-3)^2 = 9\)[/tex].
- Multiply by 5: [tex]\(5 \cdot 9 = 45\)[/tex].
- Divide 63 by -9: [tex]\(63 \div (-9) = -7\)[/tex].
- Combine the terms: [tex]\(45 + (-7) = 38.0\)[/tex].
Result: [tex]\(38.0\)[/tex]
5. Evaluate [tex]\(7 - 6 \cdot (9^2 - 5) - (-2)\)[/tex]
- Calculate the exponent: [tex]\(9^2 = 81\)[/tex].
- Subtract inside the parentheses: [tex]\(81 - 5 = 76\)[/tex].
- Multiply by -6: [tex]\( -6 \cdot 76 = -456\)[/tex].
- Combine the terms: [tex]\(7 - 456 + 2 = -447\)[/tex].
Result: [tex]\(-447\)[/tex]
6. Evaluate [tex]\((-5) - (-4) \cdot (2^3 - (-3))\)[/tex]
- Calculate the exponent: [tex]\(2^3 = 8\)[/tex].
- Add inside the parentheses: [tex]\(8 + 3 = 11\)[/tex].
- Multiply by -4: [tex]\( -4 \cdot 11 = -44\)[/tex].
- Combine the terms: [tex]\(-5 + 44 = 39\)[/tex].
Result: [tex]\(39\)[/tex]
Thus, the computed values for all expressions are summarized as follows:
[tex]\[ \begin{array}{||r|r|} \hline \multicolumn{2}{|c|}{ Order of Operations: Add, Subtract, Multiply, Divide, Parentheses and Exponents } \\ \hline \hline Evaluate each of the following. \\ \hline(2-4)^2-7 = -3 \ & 6 \cdot 9^2+5 = 491 \\ \hline (-7)^2-7(-7)-9 = 89 \ & 5(-3)^2+63 \div (-9) = 38.0 \\ \hline 7-6(9^2-5)-(-2) = -447 \ & (-5)-(-4)(2^3-(-3)) = 39 \\ \hline \end{array} \][/tex]
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