This task was designed for use with early secondary pupils, who are doing their first learning around power notation. It could equally be used with older pupils. My rationale is that I would like pupils to stumble upon some of the ideas around laws of indices in advance of studying them formally, later on. I don’t want to just present these laws as a given. I want pupils to have space to make conjectures and own the learning of the mathematics.

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Credit: @chrismcgrane84