Expert: Sherman D. - 11/11/2004

Question
1) (4^7/2 - 49^1/2)^-1/2
2) (1000/27)^2/3
3) (-2x^-1)^-3

Answer
1.)
((4^(7/2)) - (49^(1/2)))^(-1/2)
4^(7/2) = (4^7)^(1/2) = 16384^(1/2) = 128
49^(1/2) = 7
so this becomes
(128 - 7)^(-1/2)
121^(-1/2)
same as saying
1/(121^(1/2))
so the answer is ±1/11

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2.)
(1000/27)^(2/3)
becomes
(1000^(2/3))/(27^(2/3))
1000^(2/3) = (1000^2)^(1/3) = 1000000^(1/3) = 100
27^(2/3) = (27^2)^(1/3) = 729^(1/3) = 9
so the answer is 100/9 or 11 1/9

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If by this you mean

3.) (-2 * x^(-1))^(-3)
-2^(-3) * x^(-1 * -3)
-2^(-3) * x^3
becomes
(1/(-2^(-3))) * x^3
(1/(-8)) * x^3
so the answer is
(-1/8)x^3 or ((-x^3)/8)

also in case you didn't know

(x/y)^z = (x^z)/(y^z)
(xy)^z = (x^z)(y^z)
(x^y)^z = x^(yz)
(x^y)(x^z) = x^(y + z)

but when you add or subtract like in #1, you have to work it out before you can work the exponents.