Math Problem Statement

Ordena las expresiones de menor a mayor: 2^3 - 2^1, 2^1 + 3^1, 3^2.

Solution

The problem asks to "Ordena las expresiones de menor a mayor" (Arrange the expressions from smallest to largest).

Expressions:

  1. 23212^3 - 2^1
  2. 21+312^1 + 3^1
  3. 323^2

Step-by-step evaluation:

  1. 23212^3 - 2^1:

    • 23=82^3 = 8
    • 21=22^1 = 2
    • 82=68 - 2 = 6
  2. 21+312^1 + 3^1:

    • 21=22^1 = 2
    • 31=33^1 = 3
    • 2+3=52 + 3 = 5
  3. 323^2:

    • 32=93^2 = 9

Final comparison:

  • 21+31=52^1 + 3^1 = 5
  • 2321=62^3 - 2^1 = 6
  • 32=93^2 = 9

Ordered from smallest to largest:

  • 21+312^1 + 3^1 (5)
  • 23212^3 - 2^1 (6)
  • 323^2 (9)

Answer:

The expressions in ascending order are: 21+31,2321,322^1 + 3^1, \, 2^3 - 2^1, \, 3^2

Would you like a detailed explanation of any part? Let me know!


Here are five related questions to expand understanding:

  1. How would the order change if one of the bases was negative?
  2. What happens if exponents are fractional instead of integers?
  3. How do we arrange expressions involving logarithms from smallest to largest?
  4. Can you calculate the order of 42324^2 - 3^2, 24+132^4 + 1^3, and 52105^2 - 10?
  5. Why do we calculate powers before addition or subtraction in math?

Tip:

Always follow the order of operations (PEMDAS/BODMAS) when solving expressions with powers and basic operations.

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Math Problem Analysis

Mathematical Concepts

Exponents
Order of Operations

Formulas

a^b (Exponential calculation)
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 6-8