Very Easy maths question on exponents?

625^-3/4 i know this equals 1/125



for (-32)^3/5 this equals -8 right? I was wondering if someone could explain to me what happens to the 1 and why it is not needed in the answer, but compared to the top one it is needed.
first, yes (-32)^(3/5) = -8

the difference between the two is the negative sign in the exponent.

if you ignore the negative sign at first, you get 125^(-1)...

In other words 625^( 3/4) is 125.



Any number to a -1 power will be equal to one divided by the number. Its a standard exponent property.
The first question, the exponent is negative, according to the exponent rule you have to put it under 1 as a fraction.



Second question, the exponent is positive therefore no fraction is needed.
we know that 10^-2= 10^2 so similarly:



625^-3/4 = 1/ (625^3/4)



obviously 5^4=625 thus



1/(625^3/4) = 1/(5^4^(3/4))



we know 2^5^3= 2^(5*3) = 2^15, similarly



1/(5^4^(3/4) = 1/5^(4*3/4) = 1/5^3



5^3 = 125 therefore



1/5^3 = 1/125



proved



cheers