Easily Calculate 9ⁱ+9²+9³+9⁴+9⁵
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Another one from YouTube, with an easy way to calculate.
Just notice that 9ⁱ+9²=9+81=90, and find easily that 9³=9×9×9=81×9=729, then

  9ⁱ+9²+9³+9⁴+9⁵ = 90+729+9³(9ⁱ+9²)
                 = 90+729+729×90
                 = 90+729×90+729
                 = 1×90+729×90+729
                 = (1+729)×90+729
                 = 730×90+729
                 = 73×10×9×10+729
                 = 73×9×10×10+729
                 = (70+3)×9×100+729
                 = (70×9+3×9)×100+729
                 = (630+27)×100+729
                 = 657×100+729
                 = 657×100+7×100+29
                 = (657+7)×100+29
                 = 664×100+29
                 = 66400+29
                 = 66429