What is the radical expression of
1. (11)^-3/2
2. 2^(-1.5)
Thanks
I will do one.
the exponent 3/2 means sqrt of something cubed.
So (11)^-3/2 = 1/(11)^ 3/2 =1/ sqrt 11^3
= 1/ sqrt (11^2 * 11)= 1/ (11 sqrt 11)
To find the radical expression of (11)^(-3/2), we need to think about the meaning of the exponent -3/2.
An exponent of -3/2 represents the reciprocal of the square root of the base raised to the power of 3. In this case, the base is 11.
To simplify this expression, we can rewrite it as 1 divided by the square root of 11 raised to the power of 3.
So, (11)^(-3/2) = 1 / (sqrt(11))^3
To further simplify, we can write 11 as the square of sqrt(11):
(11)^(-3/2) = 1 / (sqrt(11))^3 = 1 / (11 * sqrt(11))
Thus, the radical expression of (11)^(-3/2) is 1 / (11 * sqrt(11)).
Now, let's move on to the second question:
2. 2^(-1.5)
The exponent -1.5 represents the reciprocal of the square root of the base raised to the power of 1.5.
To simplify this expression, we can rewrite it as 1 divided by the square root of 2 raised to the power of 1.5.
So, 2^(-1.5) = 1 / (sqrt(2))^1.5
To further simplify, we can write 2 as the square of sqrt(2):
2^(-1.5) = 1 / (sqrt(2))^1.5 = 1 / (2 * sqrt(2))
Thus, the radical expression of 2^(-1.5) is 1 / (2 * sqrt(2)).