negative fractional exponents

fastordie wrote:I'm having the worst time coming up with the answer. Please help.

(sqrt (6.4 * 10^-n)^(-1/3)) = 5 When n=?

Thanks

First take the left part

(sqrt (6.4 * 10^-n)^(-1/3))

(6.4 / 10^n)^ 1/2*-1/3=> (6.4 /10^n)^-1/6

=>64/(10^n+1))^-1/6 =>( (10^n+1) * 64)^1/6

=> ( (10^n+1) / 64)^1/6 =>( (10^n+1) ^1/6 ) / 64^1/6
=>( (10^n+1) ^1/6 ) /2 = 5 (As per the given)

(10^n+1) ^1/6 =10

(10^n+1 ) =10^6

=> n+1=6 => n=5

Hope it helps

stubbornp wrote: First take the left part

(sqrt (6.4 * 10^-n)^(-1/3))

(6.4 / 10^n)^ 1/2*-1/3=> (6.4 /10^n)^-1/6

=>64/(10^n+1))^-1/6 =>( (10^n+1) * 64)^1/6

=> ( (10^n+1) / 64)^1/6 =>( (10^n+1) ^1/6 ) / 64^1/6
=>( (10^n+1) ^1/6 ) /2 = 5 (As per the given)

(10^n+1) ^1/6 =10

(10^n+1 ) =10^6

=> n+1=6 => n=5

Hope it helps

how did you go from ( (10^n+1) * 64)^1/6 to ( (10^n+1) / 64)^1/6 ???
I think you may have left off a sign or something.

What I did.