Simplify expression. Write answer with positive exponents. Assume that all variables represent positive real

Question

-25^-3/2

Answer 1

-25-³/² = 1/\/-25³ = 1 over -25sqrt-25
...
??

Answer 2

The answer depends on whether by -25^-3/2 you really mean - (25)^(-3/2) or (- 25)^(-3/2), and NOT something like [-25^(-3)] / 2 . Such possible ambiguities are best avoided by the careful use of parentheses or brackets, to make your meaning CRYSTAL CLEAR !

In the first case, - (25)^(-3/2), it's - (5^2)^(-3/2) = - 5^(-3) = - 1 / 5^3 or - 1/625.

In the second case, (- 25)^(-3/2), it's (5^2)^(-3/2) = 5^(-3) = 1 / 5^3 or 1/625.

I won't even go into the third case.

Live long and prosper.

Answer 3

So keep in mind that radicals would be written as exponents, so the sq. root of a is comparable to a^(a million/2). So your subject is comparable to: a^(5/10)*(ab)^(a million/4)=a^(a million/2)*a^(a million/4)*b^... so as that's equivalent to the fourth root of (a^thrice b).

Answer 4

-25^(-3/2)
-1/(25^(3/2))
-1/((sqrt(25))^3)
-1/(±5^3)
1/125 or -1/125

Answer 5

1/-15625^1/2