by an integer power

USAGE SUMMARY

The phrase "by an integer power" is correct and usable in written English.
It can be used in mathematical contexts to describe raising a number to a whole number exponent. Example: "The function grows rapidly as it is multiplied by an integer power of x."

✓ Grammatically correct

Science

Wiki

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

A common set of decimal-based prefixes that have the effect multiplication or division by an integer power of ten can be applied to units which are too large or too small for practical use.

Wikipedia

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

Note that a superscript d is used for specifying the dimension to which a variable belongs and it is by no means of being an integer power.

EURASIP Journal on Advances in Signal Processing

If we solve recursively for this equation in terms of an integer power series by using the initial data, then the resulting solution will tend to the solutions of the second order linear differential equation: (533).

Advances in Difference Equations

It is axiomatic that the burning time dependence on particle size follows an integer power law dependence.

Combustion and Flame

Two algorithms are developed to efficiently construct hierarchical carry lookahead adders for the case when M is not an integer power or an integer multiple of n.

Microelectronics Journal

The model predicts that cancer incidence, I, will increase as an integer power of attained age, a, with the integer, depending on the number of stages, k, required for cancer induction.

Environmental Health Perspectives

In other words, a repetition is a primitively-rooted integer power u e which is not followed by another occurrence of u; and a maximal repetition is a primitively-rooted integer power u e which is not followed or preceded by another occurrence of u.

Algorithms for Molecular Biology

Finally, let τ K divided by the oversampling factor ρ; the nearest integer power of 2 to the result is the estimated subcarrier number K, which is represented as K = arg min 2 i τ K / ρ − 2 i, i = 0, 1, 2 …. (18).

EURASIP Journal on Wireless Communications and Networking

A fractional polynomial was used to relate the odds of death to PRBCs received by logistic regression; these polynomials allow great flexibility by combining combinations of integer powers (such as squares and cubes) and noninteger powers such as one-half (square root), one third (cubic root), and others.

Critical Care

"My problem," he wrote, "is that I have been persecuted by an integer.

The Guardian - Tech

The orbits are labeled by an integer, the quantum number n.

Encyclopedia Britannica

Expert writing Tips

Best practice

When describing mathematical operations, use "by an integer power" to clearly indicate scaling through exponentiation with a whole number.

Common error

Avoid using "by an integer power" when the exponent is a fraction or a decimal. In such cases, use "by a real number power" or specify the fractional exponent directly.

Linguistic Context

The phrase "by an integer power" functions as an adverbial modifier, specifying the manner in which a quantity is scaled. This is based on examples provided by Ludwig and its ability to analyze sentence structure and identify grammatical roles.

Expression frequency: Rare

Frequent in

Science

50%

Wiki

50%

News & Media

0%

Less common in

Formal & Business

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

The phrase "by an integer power" is a grammatically correct way to describe scaling a quantity through exponentiation using a whole number exponent. As noted by Ludwig, its use is relatively rare, but primarily occurs in scientific and technical contexts. When using the phrase, ensure that the exponent is indeed an integer, as using non-integer exponents requires different phrasing. Common alternatives include "to an integer exponent" and "with an integer power", though the specific choice may depend on the context and desired emphasis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

to an integer exponent

Changes the preposition from "by" to "to" and replaces "power" with "exponent".

with an integer power

Replaces "by" with "with", altering the phrase's emphasis.

multiplied by a whole number exponent

Substitutes "integer" with "whole number" for clarity, and uses "exponent" instead of "power".

divided by a whole number exponent

Changes "multiplied" to "divided".

raised to a power of an integer

Rephrases the sentence to emphasize the action of raising to a power.

scaled by an integer power

Uses "scaled" to indicate multiplication or division.

with an exponent that is an integer

Breaks down the phrase to explicitly state that the exponent is an integer.

an integer power scaling factor

Modifies the phrase to describe an integer power used as a scaling factor.

using an integer exponential value

Replaces power with exponential value.

expressed as an integer power

Focuses on the result of expressing something in terms of an integer power.

FAQs

What does "by an integer power" mean?

It means a value is being multiplied or divided by a base number raised to a whole number exponent (e.g., multiplied by 2³ or divided by 10²).

How to use "by an integer power" in a sentence?

You might say, "The function's complexity increases as it grows "to an integer exponent"." or "The signal is scaled "with an integer power" of 2 for efficient processing."

What can I say instead of "by an integer power"?

Alternatives include "to an integer exponent", "with an integer power", or "raised to a power of an integer" depending on the specific context.

Is "by an integer power" the same as "by a real number power"?

No, "by an integer power" specifically refers to using a whole number as the exponent, whereas "by a real number power" includes fractions and decimals as exponents.