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by Brent@GMATPrepNow » Thu Jan 21, 2010 7:34 pm
apuso wrote:If 3^(6x) = 8,100, what is the value of (3^(x - 1))^3 ?

A. 90
B. 30
C. 10
D. 10/3
E. 10/9
First let's simplify [3^(x-1)]^3
Using the power of a power rule [3^(x-1)]^3 = 3^(3x-3)
Using the product rule in reverse, we see that 3^(3x-3) = [3^(3x)][3^(-3)]
Now let's use the equation 3^(6x) = 8,100 to determine the value of 3^(3x)

First, we can rewrite 3^(6x) as [3^(3x)]^2 so we get [3^(3x)]^2 = 8100, which means 3^(3x) = 90

Now, we know that [3^(3x)][3^(-3)] = [90][3^(-3)] = 90/27 = 10/3
Brent Hanneson - Creator of GMATPrepNow.com
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