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

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What is the remainder when 9^6 - 11 divided by 8?

plz b fast.......i stuck up at this question....
9 = 1 (mod 8)



right? Well, then:



9^6 = 9 * 9 * 9 * 9 * 9 * 9 = 1 * 1 * 1 * 1 * 1 * 1 = 1 (mod 8)



So:



9^6 - 11 = 1 - 3 = 6 (mod 8)
(9^6-11) / 8



=(531,441-11) / 8

=531,430 / 8

=66428.75
=

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So according to vertical motion, you add the accelaration to the initial velocity forever. Therefore, if the initial velocity is 6 and accelaration is -1, it should be:

6, 5, 4, 3, 2, 1, 0 (and that would make a total of 21) every second

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