2007-02-17 04:09:54 · 4 answers · asked by Courntey c 1 in Science & Mathematics ➔ Mathematics
(4/9)^(-1.5)
4/9 = (2/3)^2
(4/9)^(-1.5) = (9/4)^(1.5)
(3/2)^(2*1.5)
(3/2)^(3)
27/8
2007-02-17 05:09:10 · answer #1 · answered by lizzie 3 · 1⤊ 0⤋
(4/9)^-1.5 = 27 / 8 = 3 3/8 = 3.375.
Two facts are needed to evaluate this :
A.) x^(-a) = (1/x)^a ; and B.) 4 = 2^2 and 9 = 3^2.
Those facts are used, successively, below:
(4/9)^-1.5 = (9/4)^1.5 =[(3^2)/(2^2)]^1.5 = 3^3 / 2^3
= 27 / 8 = 3 3/8 = 3.375. QED
Live long and prosper.
2007-02-17 04:50:29 · answer #2 · answered by Dr Spock 6 · 0⤊ 0⤋
(4/9)^-1.5 =
(4/9)-³/² =
Invertion:
\/(9/4)³ =
\/[(3/2)²]³ =
Cancelling exponents 2, remainder (3/2)³. That's equal 27/8.
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2007-02-17 14:33:58 · answer #3 · answered by aeiou 7 · 1⤊ 0⤋
note that 1.5 may be written as 3 / 2. This gives:-
(4/9)^(3/2)
the 3 indicates to the power 3
the 2 indicates square root of
Take square root first to give:-
(2/3) ^ (-3) = 1 / (8 / 27) = 27 / 8
2007-02-17 05:33:27 · answer #4 · answered by Como 7 · 1⤊ 0⤋