which number is bigger? 5 to the 20th power or 10 to the 15th power?and how can you tell?

Answer 1

Here's a method that doesn't require any calculations that you can't do easily in your head:

Start out the way some other responders have:
5^20 = 5^15 x 5^5
10^15 = 5^15 x 2^15

Since both numbers include 5^15, we just have to compare the other part of each number, i.e., 5^5 vs. 2^15

Now, 2^15 = (2^3)^5 = 8^5

So the question becomes, which is larger, 5^5 or 8^5.
Obviously, it's 8^5, which was part of 10^15, so 10^15 is larger than 5^20.

Hope that makes it as clear as possible.

Answer 2

Sounds tricky doesn't it? However, here is the simplest way to compare the two---
when you say: 10 to the 15th power it means
a numeral 1 with 15 zeros following it before putting a decimal point. i.e. 1,00000,00000,00000.0 OR a 10 with 14 zeros following. 10,0000,00000,00000
Now! determine a power of 5 that is easy to calculate in your head (or quickly with a pencil and paper): say-- 5 to the 4th power which is 625 or 5 to the 5th power which is 3125. If we use the number 3125 then we have changed the form of our 5 to the 20th to (5 to the 5thpower) with that answer raised to the 4th
power. i.e. (5 to5th) to 4th! (powers multiply-- example 2 to the 10th power is the same as (2 to the 2nd) raised to the 5th power or (2 to the 5th) raised to the 2nd power! So-- if we now have ((5 to 5th) to 4th)) you are looking at 3125 to the 4th power! To do it quickly-- call it 4000 to the 4th power. i.e. (4 x1000)to the 4th -- 4 to the 4th is 256-- 1000 to the 4th is 10 to the 3rd to the 4th-- which is 10 to the 12th! So for 5 to the 20th you will have 256 with 12 zeros following it. Now-- move the decimal point in the 256 two places so it reads 2.56 and add the two places to the 12 zeros! You will have 2.56 with 14 zeros following it. That is still less than 10 with 14 zeros following it even though you used a value for (5 to the 5th) that was larger than the actual number. (3125 to the 4th power is slightly less than 96.04 with 12 zeros following. or-- 0.96 with 14 zeros- i.e. only 1/10th as big!

Answer 3

I like this explanation best:

5^20 = 5^5 * 5^15
10^15 = 2^15 * 5^15 = (2^3)^5 * 5^15 = 8^5 * 5^15

so clearly 10^15 is bigger since 8 > 5

(actuator beat me to it)

Answer 4

well 10^15 is 2^15*5^15
2^15 is 32768 and
and 5^20/5^15 is 5^5 which is 3125 so 10^15th is the greater number.

Answer 5

5^20 vs. 10^15 = 2^15 x 5^15

so you are comparing 5^5 vs. 2^15
5^5 = 3125
2^15 = 1024 x 32 > 3125

Therefore 10^15 is bigger.

Answer 6

Computers solve this by first converting everything to binary (power of 2). To do that, you can use this trick:

N = 2 ^ X where X = log(N) / log(2)

Now find X for N=5 and N=10:

log(5) / log(2) = 2.32
log(10) / log(2) = 3.32

Which is bigger?

2.32 * 20 or 3.32 * 15

46.4 < 49.8

Therefore 5^20 < 10^15

Answer 7

10^15=2^15*5^15. So you just need to compare 5^5 and 2^15. 5^5 happens to be 3125, 2^15 is over 32,000 so the answer is 10^15.

Answer 8

10^15 power is bigger. they way that i found out was by punching the numbers into a calculator.

Answer 9

5^20 =
5^(5 * 4)
(5^4)^5
625^5

10^15 =
(5 * 2)^15
5^15 * 2^15
5^(5 * 3) * 2^15
(5^3)^5 * 2^15
125^5 * 2^15
250^5 * 2^10
500^5 * 2^5
1000^5

so as you can see 10^15 is greater than 5^20

Answer 10

10 the the 15th power is bigger just multiplyed all on the computer and every one else already told you why..