Easy Algebra Step-by-Step

46 Easy Algebra Step-by-Step

of the number; read 53 as “fi ve cubed.”

Beyond the third power, read 54 as “fi ve

to the fourth,” read 55 as “fi ve to the fi fth,”

read 56 as “fi ve to the sixth,” and so on.

Problem Write the indicated product as an exponential expression.

a. 22222222222222222

b. − 333333 ⋅− ⋅− ⋅− ⋅− ⋅−

Solution

a. 22222222222222222

Step 1. Count how many times 2 is a factor.

22222222222222222

Seven factors of 2



Step 2. Write the indicated product as an exponential expression with 2 as

the base and 7 as the exponent.

22222222222222222 = 27

b. − 333333 ⋅− ⋅− ⋅− ⋅− ⋅−

Step 1. Count how many times − 3 is a factor.

−

−

333333 ⋅− ⋅−⋅− ⋅−⋅−

Six factors of 3

  

Step 2. Write the indicated product as an exponential expression with − 3 as

the base and 6 as the exponent.

− 333333 ⋅− ⋅−⋅− ⋅−⋅− =()−^6

In the above problem, you must enclose the − 3

in parentheses to show that − 3 is the number that is

used as a factor six times. Only the 3 will be raised

to the power unless parentheses are used to indicate

otherwise.

Problem Evaluate.

a. 25

b. ()^5

c. (.. 6 )^2

())))^66 ≠≠≠− 33. ())^6 = 729 ,but

−= 36 − 729.

Don’t multiply the base by the exponent!

552 ≠⋅ 5210 ,^553 ≠⋅ 5315 ,^554 ≠⋅ 54 20 ,^

etc. xn≠⋅xn.