Simplify: left-parenthesis 27 right-parenthesis Superscript negative StartFraction 4 over 3 EndFraction Baseline
Answer options with 5 options
A.
negative StartFraction 1 over 81 EndFraction
B.
StartFraction 1 over 81 EndFraction
C.
81
D.
negative 81
E.
negative 36
The correct answer is E. negative 36.
To simplify (27)^(-4/3), we can rewrite 27 as 3^3.
(3^3)^(-4/3) = 3^(3*(-4/3))
Using the property (a^m)^n = a^(m*n), we can simplify further:
3^(3*(-4/3)) = 3^(-4)
Since a negative exponent indicates taking the reciprocal, we have:
3^(-4) = 1/(3^4) = 1/81
Lastly, since the original expression had a negative exponent, the final answer is negative:
negative 1/81 = negative 36/1 = negative 36
u sure
I apologize, I made an error in my previous response. Let me correct it.
To simplify (27)^(-4/3), we can rewrite 27 as 3^3.
(3^3)^(-4/3) = 3^(3*(-4/3))
Using the property (a^m)^n = a^(m*n), we can simplify further:
3^(3*(-4/3)) = 3^(-4)
Since a negative exponent indicates taking the reciprocal, we have:
3^(-4) = 1/(3^4) = 1/81
Therefore, the correct answer is A. negative (1/81).