###### Asked in Math and ArithmeticAlgebraIrrational Numbers

# What are the numbers from 1 to 1000 that can be expressed as a power?

## Answer

###### Wiki User

###### October 09, 2007 10:25AM

They can all be expressed as themselves to the power one, but to
make the problem interesting let's specify that the exponent has to
be an integer greater than 2. The highest exponent we are going to
need is the highest integer solution to 2p < 1000. Which is in
fact p = 9. [29 = 512.] The highest base we are going to need is
the highest integer solution to b2 < 1000. This is given by b =
31. [312 = 961.] But the only real way to answer the question is
just to get stuck in. **1** = 12

**4** = 22

**8** = 23

**9** = 32

**16** = 24 = 42

**25** = 52

**32** = 25

**36** = 62

**49** = 72

**64** = 26 = 43 = 82

**81** = 34 = 92

**100** = 102

**121** = 112

**125** = 53

**128** = 27

**144** = 122

**169** = 132

**196** = 142

**216** = 63

**225** = 152

**243** = 35

**256** = 28 = 44 = 162

**289** = 172

**324** = 182

**343** = 73

**361** = 192

**400** = 202

**441** = 212

**484** = 222

**512** = 29 = 83

**529** = 232

**576** = 242

**625** = 54 = 252

**676** = 262

**729** = 36 = 93 = 272

**784** = 282

**841** = 292

**900** = 302

**961** = 312

**1000** = 103

Well, they're all there. 41 different numbers in total.