Squares and Cubes

Two exponents have names of their own. A number to the power 2 is squared: ${5}^{2}$, read five squared, is $5\cdot 5$, which is 25. The name comes from geometry. A square with sides 5 long holds 5 rows of 5 small unit squares, so its area is ${5}^{2}$.

A number to the power 3 is cubed: ${3}^{3}$, three cubed, is $3\cdot 3\cdot 3$, which is 27. A cube with edges 3 long is built from 3 layers, each a 3 by 3 square of small cubes, so its volume is ${3}^{3}$.

When powers sit in a sum, work out each power first and add after: ${5}^{2}+{3}^{3}$ becomes $25+27$, which is 52. Each power is one number in a compact package, so it has to be opened before it can be added.