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Precision of a number raised to a power

• To: mathgroup at smc.vnet.net
• Subject: [mg73501] Precision of a number raised to a power
• From: Sonya <sonyaBabken at yahoo.de>
• Date: Tue, 20 Feb 2007 06:20:37 -0500 (EST)

Hallo
I am new to Mathematica and I am thankful to any help regarding the following.
If I have something like a^b . The a is any arbitrary decimal number (let us say of precision double) the b are numbers from 1-10 (exact numbers without a point). 
What will be the precision of the above expression after raising a to the powers from 1-10.

Many thanks in advance
Sonya