Exponents problem

[proton742]

What are all possible ways of writing 1/64 as an integer raised to an integer power?

Explain why each expression you found equals 1/64, and try to explain why there are no other possibilities besides the ones you found.

I have been struggling with this problem for a while and would appreciate help. Thank you!

 

[mmm4444bot]

I have been struggling with this problem for a while

Hello. Did you start by writing Integer powers that yield 64? Have you thought about possibility of having negative bases? Is it possible to have both even and odd bases? Please share what you've tried or thought about so far. Thank you!

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[Deleted member 4993]

What are all possible ways of writing 1/64 as an integer raised to an integer power?

Explain why each expression you found equals 1/64, and try to explain why there are no other possibilities besides the ones you found.

I have been struggling with this problem for a while and would appreciate help. Thank you!

Start with

64 = 8^2 = 4^3 = 2^6 ..... Continue..

 

[Steven G]

You really have to try. You should know that (1/64)¹ = 1/64. How about 64^-1 = 1/64? Any others?