Powers of numbers and logs

it takes longer to write 7 x 7 than 72 72 is called seven squared , because it relates to the area of a square. Notice the notation 72 means 7 multiplied by another 7 = 7 x 7 = 49. 

This is a very useful notation. Let us extend it - what is 73 The logical extension is that it relates to a cube. A cube has equal sides. Its volume is length x breadth x height, so the volume of the cube = 7 x 7 x 7 = 343 and 73 is called seven cubed . 

If 33 = three cubed = 3 x 3 x 3 = 27, then 74 must mean 7 x 7 x 7 x 7 = 2401, i.e. four sevens multiplied by each other. What are we going to call this, since 74 has no relationship to a real object We know about squares and cubes - squares have equal sides and are flat - cubes have equal sides and occupy space. There is no name with a real object for 74 , so it is called seven to the power 4 or seven to the fourth . 

We (for the most part) have 10 digits and our numbering system is based on 10  

104 = 10 x 10 x 10 x 10 = ( 10 to the power 4 or 10 to the fourth = 10 000) By this time you might have noticed that the power to which 10 is raised on the left-hand side is the same as the number of zeros in the answer. 

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