How do I evaluate 9 to the power of 100 using a step other than multiplying 9 again and again?

Question

Are than any steps or shortcuts which will help me get the answer easier other than multipying it over and over again.

Answer 1

You could write it as 3 to the power of 300. :P
Or you could say 81 to the power of 50, then 81squared to the power of 25, and so on....

Answer 2

9^100 = (9 ^ 50)^2 = (9 ^ 25)^ 4 =
= (9 * 9^24)^4 = [9 * (9 ^ 12)^2]^4 =
= [9 * (9^6)^4]^4 = [9 * (9^3)^8]^4

i. 9^3 = 729
ii. Square the result of (i) 3 times
iii. Multiply the result of (ii) by 9.
iv. Square the result of (iii) 2 times.

Answer 3

You get yourself a TI-89 calculator and you type in 9^100 and you watch with wide-eyed amazement as it gives you an exact integer answer with all of those digits.

There is no other shortcut, I'm afraid.

Answer 4

well if you're using a calculater you can put in 9 (then the power of, which usually looks like an x and y on top of each other) then 100. it will automatically do the sum for you. you need a scientific calculator to do this though

Answer 5

9^100 take the log and get
100 log(9) = 95.42425094 = 10^(.42425094) * 10^95
2.656139865 * 10^95
Unless you -need- all 96 digits ☺

Doug

Answer 6

(9^25)^4 = [(9^5)^5]^4

Ilusion

Answer 7

Use a calculator