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Simplify the following expressions: e) (3)2 2 - 22 3, f) 5 * (2 + 3)2 + 13, a) 62 - 42 - sqrt(9).

Mathematics

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Answers

2 parts
e

6\text{6}

f

126\text{126}

17\text{17}

Step-by-step solution

12 steps

Here are the solutions for the expressions:

Part e· 4 steps

Simplify (3)2×2−22×3(3)^2 \times 2 - 2^2 \times 3.

  1. Evaluate the exponents.

    (3)2=9(3)^2 = 9 22=42^2 = 4
  2. Substitute the values back into the expression.

    9×2−4×39 \times 2 - 4 \times 3
  3. Perform the multiplications from left to right.

    9×2=189 \times 2 = 18 4×3=124 \times 3 = 12
  4. Perform the subtraction.

    18−12=618 - 12 = 6

    The simplified expression is:

    6\boxed{\text{6}}

Part f

126\text{126}

Simplify 5×(2+3)2+135 \times (2 + 3)^2 + 1^3.

  1. Perform the operation inside the parentheses.

    (2+3)=5(2 + 3) = 5
  2. Evaluate the exponents.

    52=255^2 = 25 13=11^3 = 1
  3. Substitute the values back into the expression.

    5×25+15 \times 25 + 1
  4. Perform the multiplication.

    5×25=1255 \times 25 = 125
  5. Perform the addition.

    125+1=126125 + 1 = 126

    The simplified expression is:

    126\boxed{\text{126}}

    Activity 2, a) Simplify 62−42−96^2 - 4^2 - \sqrt{9}.

  6. Evaluate the exponents and the square root.

    62=366^2 = 36 42=164^2 = 16 9=3\sqrt{9} = 3
  7. Substitute the values back into the expression.

    36−16−336 - 16 - 3
  8. Perform the subtractions from left to right.

    36−16=2036 - 16 = 20 20−3=1720 - 3 = 17

    The simplified expression is:

    17\boxed{\text{17}}
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