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I'm using the Interpolation plug-in in QGIS 2.18 to perform IDW Interpolation. I was hoping to specify a power of 2 and use the 10 nearest points to calculate the output, but I don't necessarily see a way to do so.

Is there another tool that I can use to accomplish this?

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If you go into Raster Tools>Analysis. There's Grid(interpolation), That should work.

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Goto Raster > Interpolation > Interpolation

Select IDW interpolation method and click on the wrench icon on the right. It prompts you to enter distance coefficient. Choose this value wisely.

Refer the answer in this link.

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