Math Problem Statement

Solve the mathematical expressions provided in the image (problems 16–20).

Solution

I see the image contains five mathematical expressions (problems 16–20). Let's solve them one by one:

16. (121835)×(4)\left( \frac{12 - 18}{3 - 5} \right) \times (-4)

  1. 1218=612 - 18 = -6
  2. 35=23 - 5 = -2
  3. 62=3\frac{-6}{-2} = 3
  4. 3×(4)=123 \times (-4) = -12

Solution for 16: 12-12


17. (2424)(36)÷(2)(2^4 - 24) - \left( \sqrt{36} \right) \div (-2)

  1. 24=162^4 = 16
  2. 1624=816 - 24 = -8
  3. 36=6\sqrt{36} = 6
  4. 6÷(2)=36 \div (-2) = -3
  5. 8(3)=8+3=5-8 - (-3) = -8 + 3 = -5

Solution for 17: 5-5


18. 32+144(2)5+643-3^2 + \sqrt{144} - (-2)^5 + \sqrt[3]{-64}

  1. 32=9-3^2 = -9 (Exponent takes precedence)
  2. 144=12\sqrt{144} = 12
  3. (2)5=32(-2)^5 = -32
  4. 643=4\sqrt[3]{-64} = -4
  5. 9+12(32)+(4)-9 + 12 - (-32) + (-4)
  6. 9+12+324=31-9 + 12 + 32 - 4 = 31

Solution for 18: 3131


19. {\left[(-15 + 5) \times 2 + 8\right] - \frac{32}{8}} - (-7)

  1. 15+5=10-15 + 5 = -10
  2. 10×2=20-10 \times 2 = -20
  3. 20+8=12-20 + 8 = -12
  4. 328=4\frac{32}{8} = 4
  5. 124=16-12 - 4 = -16
  6. 16(7)=16+7=9-16 - (-7) = -16 + 7 = -9

Solution for 19: 9-9


20. (52)3×2+[4+(7)]÷(2+4)2(5 - 2)^3 \times 2 + \left[-4 + (-7)\right] \div (-2 + 4)^2

  1. 52=35 - 2 = 3
  2. 33=273^3 = 27
  3. 27×2=5427 \times 2 = 54
  4. 4+(7)=11-4 + (-7) = -11
  5. 2+4=2-2 + 4 = 2
  6. 22=42^2 = 4
  7. 11÷4=114=2.75-11 \div 4 = -\frac{11}{4} = -2.75
  8. 54+(2.75)=51.2554 + (-2.75) = 51.25

Solution for 20: 51.2551.25


Do you want more details on any of these steps, or have any further questions?

Here are 5 related problems you can try:

  1. Simplify 16937×(5)\frac{16 - 9}{3 - 7} \times (-5)
  2. Solve (325)(81)÷(3)(3^2 - 5) - \left( \sqrt{81} \right) \div (-3)
  3. Simplify 42+100(3)4-4^2 + \sqrt{100} - (-3)^4
  4. Solve {(212)×5+10}505\{(2 - 12) \times 5 + 10\} - \frac{50}{5}
  5. Solve (71)2×2+[3+(9)]÷(3+5)2(7 - 1)^2 \times 2 + [-3 + (-9)] \div (-3 + 5)^2

Tip: Always apply the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) carefully when simplifying complex expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Order of Operations
Exponents
Square Roots
Cubic Roots

Formulas

Exponentiation
Order of Operations (PEMDAS)
Square root (√x)
Cubic root (³√x)

Theorems

Order of Operations (PEMDAS)

Suitable Grade Level

Grades 9-11