Power

$\text{Result}_i = A_i^{B_i}$

Raises each element of the first input to the power of the corresponding element in the second. Essential for compound growth, volatility calculations, and non-linear scaling.

Base (A)	Exponent (B)	Result
2	3	8
4	0.5	2
10	-1	0.1
5	0	1

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Missing Data

If either input is missing (null) at a position — a data gap or a closed-market day — the result at that position is null. The module never invents a value for missing data: a gap in your inputs stays a gap in the output.

Base	Exponent	Result
2	null	null
null	3	null
null	null	null

In live execution the module returns exactly one datapoint — the newest position — which is null when it cannot be determined.

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Special Cases

⚠️ Important: Separate from missing data, a result can be mathematically undefined for real inputs:

Scenario	Result	Notes
Negative base + fractional exponent	null	Undefined in real numbers (would be complex)
0 raised to negative power	inf	Division by zero
Very large exponent	inf	Overflow

Example: $(-4)^{0.5}$ → null (would be $2i$ in complex math)

Infinite results pass through unchanged — they are values, not gaps.

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Common Exponents

Exponent	Operation	Use Case
2	Square	Variance from std dev
0.5	Square root	Std dev from variance
-1	Reciprocal	Inverse weighting
0	Any base → 1	Reset to constant

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Input Alignment

Systemic automatically aligns inputs before calculation:

Scenario	What Happens
Different lengths	Shorter series padded by repeating last value
Different frequencies	Lower-frequency upsampled to match higher
One constant	Constant expanded to match series length

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Practical Example: Compound Growth

Calculate future value with compound interest:

$\text{Future Value} = (1 + r)^n$

Annual Rate	Years	Growth Factor
5%	10	$1.05^{10} = 1.629$
7%	20	$1.07^{20} = 3.870$
10%	30	$1.10^{30} = 17.449$

Connect a growth factor series (1 + return) to the base and time periods to the exponent for dynamic compounding calculations.

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Related Modules

• SQRT — Square root (equivalent to exponent 0.5)
• MUL — Repeated multiplication
• DIV — Reciprocal (equivalent to exponent -1)

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Interpretation Tips

• Exponent > 1: Spreads out values, makes large larger and small smaller
• 0 < Exponent < 1: Compresses spread, brings extremes closer to center
• Exponent < 0: Inverts the scale (reciprocal-like)
• Exponent = 0: Everything becomes 1

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Advantages

• Non-linear transformations — Essential for many financial calculations
• Flexible — Squares, roots, reciprocals all in one module
• Element-wise — Works naturally with time series

Disadvantages

• Undefined cases — Negative bases with fractional exponents produce null
• Overflow risk — Large exponents can produce infinity
• Interpretation — Results may lose intuitive meaning at extreme exponents

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Further Reading

• Exponentiation - Wikipedia
• Volatility and Variance in Finance
• Compound Interest Formula