Exponents

Examples

• 2⁵ = 2 × 2 × 2 × 2 × 2 = 32
• 5⁷ = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78.125

Exponent Operations

Multiplication

• 10⁴ × 2² = (10 × 2)^{4 + 2} = 20⁶

Division

• 10³ ÷ 2⁴ = (10 ÷ 2)^{4 - 2} = 5²

Exponent

• (2²)³ = 2^{2 × 3} = 2⁶ = 64

Zero Exponent

a⁰ = 1

Examples

• 5⁰ = 1
• 7⁰ = 1
• 100⁰ = 1
• 28,67⁰ = 1

One Exponent

a¹ = a

Examples

• 5¹ = 5
• 7¹ = 7
• 100¹ = 100
• 28,67¹ = 28,67

Fractional Exponent

x ^y⁄_z = ^zx^y

Examples

• 5 ^1⁄₂ = ²5
• 7 ^2⁄₃ = ³7²

Small Note: 2x or x menans square root. The 2 before root should be removed. The 2 is only present for easier purposes.
3x means cubic root.

Exponential Equation

1. 2^{x + 5} = 64
   = 2^{x + 5} = 2⁶ _{↖ ubah ke bentuk 2 berpangkat (2^x)}
   = x + 5 = 6
   = x = 1
2. 16^{x + 2} = 32
   = (2⁴)^{x + 2} = 2⁵
   = 2^{4x + 8} = 2⁵
   = 4x + 8 = 5
   = 4x = 5 - 8
   = 4x = -3
   = x = ^-3⁄₄ = -³⁄₄