Answer:
(1/32)^(3/5) = 1/2^15.
(9)^(-3/2) = 1/27.
Explanation:
To simplify the expressions:
(1/32)^(3/5):
To simplify this expression, we can raise the numerator and the denominator separately to the power of 3/5.
(1/32)^(3/5) = (1^(3/5))/(32^(3/5))
The numerator simplifies to 1^3 = 1, and the denominator simplifies to (2^5)^3 = 2^(5*3) = 2^15.
Therefore, the expression simplifies to:
(1/32)^(3/5) = 1/2^15.
(9)^(-3/2):
To simplify this expression, we can take the reciprocal of 9^3/2, which is equivalent to the square root of 9 cubed.
9^(3/2) = sqrt(9^3) = sqrt(999) = sqrt(729) = 27.
Taking the reciprocal gives:
(9)^(-3/2) = 1/27.
Therefore, the simplified expression is 1/27.