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Powers, Exponents, and Roots


Introduction and Summary

Squares, Cubes, and Higher Order Exponents

Base  -  The number that is raised to a power. In " 74 ", 7 is the base.
Cube  -  A number times itself times itself. 5 cubed = 53 = 5×5×5 = 125 .
Cube Root  -  A number that, when cubed, is equal to the given number.
Exponent  -  The power to which a number is raised; the number of times a number is multiplied. In " 74 ", 7 has an exponent of 4, and 7 is multiplied 4 times (7×7×7×7) .
Fractional Exponent  -  An exponent in which the numerator is the power to which the number should be taken and the denominator is the root which should be taken.
Mean  -  The sum of two numbers, divided by 2 (sometimes called an average). This yields the number directly between the two numbers.
Negative Exponent  -  An exponent that takes the base number to the positive opposite of the exponent (the exponent with the negative sign removed), and places the result in the denominator of a fraction whose numerator is 1.
Perfect Square  -  The square of a whole number. 1, 4, 9, 16, 25, 36, 49, ... are all perfect squares.
Simplify (Square Root)  -  To remove all factors that are perfect squares from inside the square root sign and place their square roots outside the sign.
Square  -  A number times itself. 5 squared = 52 = 5×5 = 25 .
Square Root  -  A number that, when squared (multiplied by itself), is equal to the given number.