Base to Power Calculator
Calculate exponents with ease and explore advanced mathematical concepts
Basic Calculation
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Calculation Results
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Calculation Breakdown
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📚 Common Powers Reference
Powers of 2
| Exponent | Result |
|---|---|
| 2¹ | 2 |
| 2² | 4 |
| 2³ | 8 |
| 2⁴ | 16 |
| 2⁵ | 32 |
| 2⁶ | 64 |
| 2⁷ | 128 |
| 2⁸ | 256 |
| 2⁹ | 512 |
| 2¹⁰ | 1,024 |
Powers of 10
| Exponent | Result |
|---|---|
| 10¹ | 10 |
| 10² | 100 |
| 10³ | 1,000 |
| 10⁴ | 10,000 |
| 10⁵ | 100,000 |
| 10⁶ | 1,000,000 |
| 10⁻¹ | 0.1 |
| 10⁻² | 0.01 |
| 10⁻³ | 0.001 |
| 10⁻⁶ | 0.000001 |
Square Roots
| Number | √x |
|---|---|
| √1 | 1 |
| √2 | ≈1.4142 |
| √3 | ≈1.7321 |
| √4 | 2 |
| √5 | ≈2.2361 |
| √9 | 3 |
| √16 | 4 |
| √25 | 5 |
| √100 | 10 |
| √144 | 12 |
🧮 Exponent Concepts Explained
Basic Exponents
xⁿ means multiplying x by itself n times. For example, 2³ = 2 × 2 × 2 = 8.
Fractional Exponents
x^(m/n) equals the n-th root of x raised to the m power. x^(1/2) is the square root of x.
Negative Exponents
x⁻ⁿ equals 1 divided by xⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125.
Exponent Rules
xᵃ × xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ, xᵃ ÷ xᵇ = xᵃ⁻ᵇ, x⁰ = 1 for any x ≠ 0.
Special Cases
0⁰ is undefined. 1ⁿ = 1 for any n. 0ⁿ = 0 for n > 0. x¹ = x.
Exponential Growth
When x > 1, xⁿ grows rapidly as n increases. When 0 < x < 1, xⁿ decreases toward 0.
Note: This calculator provides precise mathematical calculations. For very large exponents (>10¹⁰⁰), results may be displayed in scientific notation due to JavaScript number limitations.