1. Squaring a Number

Squaring a number involves multiplying the number by itself. For example:

• 3² = 3 × 3 = 9
• 7² = 7 × 7 = 49

2. Raising to Powers

Raising a number to a power means multiplying it by itself multiple times based on the power. Examples:

• 2³ = 2 × 2 × 2 = 8
• 5⁴ = 5 × 5 × 5 × 5 = 625

3. Square Roots

The square root of a number is the value that, when squared, returns the original number. For instance:

• √16 = 4 because 4² = 16
• √81 = 9 because 9² = 81

4. Square Roots of Negatives

Negative numbers do not have real square roots because squaring any real number results in a positive value. However, imaginary numbers represent them:

• √-4 = 2i
• √-9 = 3i

5. Cube Roots

The cube root of a number is the value that, when cubed, equals the original number. Examples:

• ³√8 = 2 because 2³ = 8
• ³√27 = 3 because 3³ = 27

6. PEMDAS and Beyond

PEMDAS is an acronym that helps remember the order of operations in mathematical expressions:

1. Parentheses
2. Exponents
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Example: 3 + 2 × (4²) = 3 + 2 × 16 = 3 + 32 = 35

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