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Evaluate the following expressions: a) (4+2)2 - 2 imes (7 - 22 + 2) b) 60 + (8 rac; 4)2 - [10 - (3+2)2 rac; 5]

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2 parts
a

26\text{26}

b

0\text{0}

Step-by-step solution

11 steps

Here are the evaluations for the given expressions:

Part a· 5 steps

Evaluate (4+2)2−2×(7−22+2)(4+2)^2 - 2 \times (7 - 2^2 + 2)

  1. Evaluate the expressions inside the parentheses.

    (4+2)2−2×(7−22+2)=(6)2−2×(7−4+2)(4+2)^2 - 2 \times (7 - 2^2 + 2) = (6)^2 - 2 \times (7 - 4 + 2)

  2. Continue evaluating inside the second set of parentheses.

    62−2×(3+2)=62−2×(5)6^2 - 2 \times (3 + 2) = 6^2 - 2 \times (5)

  3. Evaluate the exponent.

    36−2×536 - 2 \times 5

  4. Perform the multiplication.

    36−1036 - 10

  5. Perform the subtraction.

    36−10=2636 - 10 = \boxed{\text{26}}

Part b

0\text{0}

Evaluate 60+(8÷4)2−[10−(3+2)2÷5]6^0 + (8 \div 4)^2 - [10 - (3+2)^2 \div 5]

  1. Evaluate the innermost parentheses.

    60+(8÷4)2−[10−(5)2÷5]6^0 + (8 \div 4)^2 - [10 - (5)^2 \div 5]

  2. Evaluate the remaining parentheses and the exponent 606^0.

    60+(2)2−[10−52÷5]=1+22−[10−52÷5]6^0 + (2)^2 - [10 - 5^2 \div 5] = 1 + 2^2 - [10 - 5^2 \div 5]

  3. Evaluate the exponents.

    1+4−[10−25÷5]1 + 4 - [10 - 25 \div 5]

  4. Evaluate the division inside the brackets.

    1+4−[10−5]1 + 4 - [10 - 5]

  5. Evaluate the subtraction inside the brackets.

    1+4−[5]1 + 4 - [5]

  6. Perform the addition and subtraction from left to right.

    5−5=05 - 5 = \boxed{\text{0}}
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