For a hypothesis to have explanatory power means that it effectively clarifies and accounts for a specific phenomenon or set of phenomena, providing a clear understanding of how and why certain events occur. Among the options you've provided, none directly define explanatory power, but we can surmise which relates to it conceptually.
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The hypothesis is testable. This is important for a hypothesis, as a testable hypothesis can be evaluated through experimentation or observation, but it doesn't directly address explanatory power.
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The hypothesis has an independent and a dependent variable. While this relates more to the structure of a hypothesis in experimental research design, it does not specifically speak to its explanatory capability.
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The hypothesis has been tested many times and over a wide variety of conditions. This option could be the closest to relevant to explanatory power. A hypothesis that has been rigorously tested and consistently provides explanations for observations across various conditions suggests a robust explanatory capacity.
In summary, a hypothesis with explanatory power helps to elucidate underlying mechanisms and can successfully account for observed patterns or phenomena in a consistent manner.