Exponents

The mathematical notations for numbers which are the result of a number that is multiplied by itself a number of times is called exponents.

Examples:

x3 = x × x × x x5 = x × x × x × x × x

The expression of xn is also called the nth power of x. The x is the base, while the n is the exponent. Math questions will usually only

utilize integral exponents. x2 is read as x-squared, and x3 is read as x-cubed. All others are read as a power of x. x4 is read as the 4th power of x.

When it comes to the power of 10, there is a simple, quick rule that simplifies the powers of 10, by writing it as 1, followed by the number of zeros as specified by the power.

Examples: 105 = 1 followed by 5 zeros. 100000 = 100,000. An example you may find is:

Represent 32,456 to the power of 10.

The solution would be as follows:

32,456 = 3 × 104 + 2 × 103 + 4 × 102 + 5 × 101 + 6 × 100

Consider the following example:

Solve for x: (x - 3)2 = 49.

You could use algebra and take the square root of both sides or since 49 is a perfect square you could guess integers for x. Just remember x -3 must be positive or negative.

If you try guessing, the integers 10 and -4 work. To get an algebra solution, do the following:

(x - 3)2 = 49

x - 3 = 7 or x - 3 = -7

x = 10 or x = -4

It is your goal to get problems correct quickly. Sometimes guessing (Guessing in this case means substituting in numbers to see which satisfy the equation.) is faster than solving an equation, if you train yourself to use the technique. Of course, if you cannot "see" the answers fast enough, use other approaches to answer the problem.