Algebra

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19 Mar 2010 15:11:58 IST

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Is x to the power 1/2007 = x to the power -2007.

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Is x to the power 1/2007 = x to the power -2007.

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Hot goIITian

Joined: 24 Feb 2010

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19 Mar 2010 15:13:38 IST

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No.It is equal to 2007th root of x

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Joined: 19 Oct 2006

Posts: 7452

19 Mar 2010 16:02:02 IST

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No this is not the case.

Rather it is like this

x ^{1 /2007} = ( 1 / x ) ^{- 1/2007}

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19 Mar 2010 16:03:33 IST

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Laws of Exponents

Here are the Laws:

Law	Example
x¹ = x	6¹ = 6
x⁰ = 1	7⁰ = 1
x^-1 = 1/x	4^-1 = 1/4

x^mxⁿ = x^m+n	x²x³ = x²⁺³ = x⁵
x^m/xⁿ = x^m-n	x⁶/x² = x^6-2 = x⁴
(x^m)ⁿ = x^mn	(x²)³ = x^2×3 = x⁶
(xy)ⁿ = xⁿyⁿ	(xy)³ = x³y³
(x/y)ⁿ = xⁿ/yⁿ	(x/y)² = x² / y²
x^-n = 1/xⁿ	x^-3 = 1/x³
And the law about Fractional Exponents:

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