Question

Why does:

(2/5)^-3 = 125/8?

I got up to 8/125, but why is it 125/8?

Answer 1

\[2^{-1}=\frac{ 1 }{ 2 }\]
so,\[(\frac{ 2 }{ 5 })^{-3}=\frac{ 1 }{ (\frac{ 2 }{ 5 })^{3} }=\frac{ 1 }{ \frac{ 8 }{ 125 } }=\frac{ 125 }{ 8 }\]

Answer 2

Thank you neer2890! :) Makes so much sense now.

Answer 3

you're welcome...:)

Answer 4

Sorry, before you go, could you please explain what happens after 1/(8/125)?

Answer 5

ok.\[\frac{ \frac{ a }{ b } }{ \frac{ c }{ d } }=\frac{ a }{ b }*\frac{ d }{ c }\]

Answer 6

when in division, we just reciprocal it and multiply with numerator

Answer 7

Thank you! :)

Answer 8

you're welcome