Common exponents

Last updated: 11 Nov 2008

We will begin with an example of an exponential, .

It is a shorthand way of writing '5 times itself 3 times'. 5 is the base, i.e. the number which is multiplied by itself. 3 is the exponent or power, i.e. the number times that the base is multiplied by itself.

It can also be referred to as

• 5 cubed or...
• 5 to the power of 3 or...
• 5 raised to the 3^rd power

In a similar way is 2 times itself 7 times.

And is y times itself 4 times.

Squares and Cubes

Squares, cubes and their respective inverses, square roots and cube roots, are the exponents that come up most regularly in the GMAT. It is therefore useful to memorize them, so as to have them at your fingertips.

Note: I have left out the cubes of 7 and above, not because they do not exist, but simply because you do not need to know them for the GMAT.

Number ( x )	Square ( x 2 )	Cube ( x 3 )
1	1	1
2	4	8
3	9	27
4	16	64
5	25	125
6	36	216
7	49	-
8	64	-
9	81	-
10	100	-
11	121	-
12	144	-
13	169	-
14	196	-
15	225	-
16	256	-

You should learn these because it will save you time and lessen your chances of making mistake when you meet them in the GMAT.

Square and Cube Roots

The square root of a number is the number which when multiplied by itself gives you the original number. For example,

...and...

Similarly the cube root of a number is that which multiplied by itself 3 times produces the original number.

For example,

...and...

Note: 64 is the smallest number (apart from 1) which is both a square and a cube, i.e. .

Next page: Properties of exponents