Easy Algebra Step-by-Step

Exponentiation 45

Step 2. Do the multiplication.

35 = 33333333333 = 243 (t he fi fth power of 3)

The following discussion tells you about the different types of exponents

and what they tell you to do to the base.

Natural Number Exponents

You likely are most familiar with natural number exponents.

Natural Number Exponents

If x is a real number and n is a natural number, then xn xxx x

nx

= xxx⋅⋅

ft f

.

For instance, 54 has a natural number exponent, namely, 4. The expo-

nent 4 tells you how many times to use the base 5 as a factor. When you

do the exponentiation, the product is the fourth power of 5 as shown in

Figure 4.2.

For the fi rst power of a number, for instance, 51 , you usually omit the expo-

nent and simply write 5. The second power of a number is the square of the

number; read 52 as “fi ve squared.” The third power of a number is the cube

P

Figure 4.1 Parts of an exponential form

Base Fifth power of 3

Exponent

35 = 3·3·3·3·3 = 243

Figure 4.2 Fourth power of 5

Base Fourth power of 5

Exponent

54 = 5·5·5·5 = 625