27 over 8 power minus 2/3
applied math
2006-10-02 04:27:46 · 7 answers · asked by Schnatzel 2 in Science & Mathematics ➔ Mathematics
(27/8)^(-2/3)
=(3/2)^[3* -2/3]
=(3/2)^(-2)
overturn the fraction n square it
=(2/3)^2
=4/9
2006-10-02 04:50:23 · answer #1 · answered by Anonymous · 0⤊ 0⤋
(27/8)^-2/3
= (3*3*3/2*2*2)^-2/3 (negative power means take the reciprocal)
= (2*2*2/3*3*3)^2/3 (raising to the power of one third means take the cube root)
= (2/3)^2 (raising to the power of 2 means take the square)
= 4/9
2006-10-02 11:43:04 · answer #2 · answered by DazerUK 2 · 0⤊ 0⤋
first you need to take (27/3) to the cube root which equals 3/2.
Then you take (3/2)^2 = 9/4
2006-10-02 11:32:21 · answer #3 · answered by redballoon 4 · 0⤊ 0⤋
(27/8)^(-2/3)
= (3^3/2^3)^(-2/3) as 27 = 3^3 and 8 = 2^3
=((3/2)^3)^(-2/3) as (a^x/b^x) = (a/b)^x
= (3/2)^(3*(-2/3)) as (a^x)^y = a^xy
= (3/2)^-2
= (2/3)^2 (as a^x = (1/a)^-x)
= 4/9
2006-10-02 12:03:47 · answer #4 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
((3/2)^3)^(-2/3)=(2/3)^2=4/9
2006-10-02 11:36:40 · answer #5 · answered by Arjun 1 · 0⤊ 0⤋
(3/2)^3*-2/3
=(3/2)^-2
2/3^2
4/9
2006-10-02 11:55:28 · answer #6 · answered by sonali 3 · 0⤊ 0⤋
(27/8)^(-2/3)
(8/27)^(2/3)
(8^(2/3))/(27^(2/3))
(cbrt(8^2))/(cbrt(27^2))
(cbrt(64))/(cbrt(729))
(4/9)
2006-10-02 12:46:36 · answer #7 · answered by Sherman81 6 · 0⤊ 0⤋