# Numerical comparisons of exponential expressions: The saliency of the base component

## TL;DR

People find it hard to compare exponential expressions, and they rely more on the base number than the power when making judgments.

## Contribution

The study reveals a base-power compatibility effect and shows that base components are more salient in exponential comparisons.

## Key findings

- Participants showed a base-power compatibility effect in comparing exponential expressions.
- Larger power distances increased the compatibility effect in both experiments.
- Base-result congruent pairs were processed faster and more accurately than power-result congruent pairs.

## Abstract

Exponential expressions represent series that grow at a fast pace such as carbon pollution and the spread of disease. Despite their importance, people tend to struggle with these expressions. In two experiments, participants chose the larger of two exponential expressions as quickly and accurately as possible. We manipulated the distance between the base/power components and their compatibility. In base-power compatible pairs, both the base and power of one expression were larger than the other (e.g., 23 vs. 34), while in base-power incompatible pairs, the base of one expression was larger than the base in the other expression but the relation between the power components of the two expressions was reversed (e.g., 32 vs. 24). Moreover, while in the first experiment the larger power always led to the larger result, in the second experiment we introduced base-result congruent pairs as well. Namely, the larger base led to the larger result. Our results showed a base-power compatibility effect, which was also larger for larger power distances (Experiments 1–2). Furthermore, participants processed the base-result congruent pairs faster and more accurately than the power-result congruent pairs (Experiment 2). These findings suggest that while both the base and power components are processed when comparing exponential expressions, the base is more salient. This exemplifies an incorrect processing of the syntax of exponential expressions, where the power typically has a larger mathematical contribution to the result of the expression.

The online version contains supplementary material available at 10.3758/s13423-024-02571-8.