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The product of a number and itself is called what of a number?
"The square" or "second power".
Why is a cube number called a cube number?
To calculate the volume of a cube, you use the third power of the length, so for example, if the length of an edge of a cube is 3" then the volume is 3x3x3 = 27 cubic inches. As a result, any time a number is raised to the third power, we can call it cubed, much as raising it to the second power is that number squared.
What is a number produced by raising a base to and exponent?
A power.
What is a rule for raising a negative number to a power?
It is the positive form of the number raised to that power, multpilied by -1 raised to that power.
Why is raising the number to the second power called squaring the number?
That's because you are multiplying it by itself. So "two, squared' means the same as 'two times two', and 'three, squared' means the same as 'three times three'. Multiplying a number by itself is exactly the same process of finding the area of a square who's dimensions are the number in question. Therefore multiplying a number by itself is known as squaring. For the same reason of raising a number to the third power is known as cubing. (Because its the same process you would use to find the volume of a cube.)
