exponents?

[guest621]

I have a question about exponents. Two questions yield different results for exponents rules. I assume I have made a calculation error and hopefully you can shed some light.

Test Code #42, page 7, #12:
Three musical notes have frequencies x, y, and z, respectively. If x, y, and z are positive, x/y = y/z, and 2x = z, what is y in terms of x?
A. 2x
B. (Sq Rt 2) * x ----Correct answer
C. 1/(Sq Rt 2) * x
D. 1/2 x
E (Sq Rt 2) / 3 * x

I understand how it is B but it seems to contradict the rules for answering the MBA software question If 4^4x = 1600, what is the value of (4^x-1)^2?

In the test code question, I solve it as x/y = y/z . Plugging in z, and then cross multiplying, I got y^2=2x^2. Thus, y = Sq Rt of (2x^2). Answer B. Great!

ALL GOOD AND ALL UNDERSTOOD. THAT SAID, MY QUESTION IS AS FOLLOWS:
In the MBA question as noted above, the Sq Rt of 4^4x is 4^2x. If so, then how can the Sq Rt of 2x^2 not equal 2x? Hope my question is clear! Thanks.

[RonPurewal]

In the MBA question as noted above, the Sq Rt of 4^4x is 4^2x. If so, then how can the Sq Rt of 2x^2 not equal 2x? Hope my question is clear! Thanks.

you're confusing two different animals, namely, the base of the exponential and the coefficient of the term. here's the deal:
the base of the exponential doesn't change
the coefficient is subjected to whatever power/root is applied to the expression

so:
in the mba example, there's no coefficient, and
√(4^4x) = 4^2x (where the base of the power doesn't change)

in the other example,
√(2x^2) = (√2)x^1 (where the coefficient gets square-rooted, but the base stays the same, just as it did before)

hope that helps.
xmas in april!

[guest612]

i think as i began to do more problems i saw that...but thanks for clarifying!

ha. christmas in april!
thanks again! sometimes my head gets all messed up with so much stuff...i think. test time is around the corner this week!

[RonPurewal]

i think as i began to do more problems i saw that...but thanks for clarifying!

ha. christmas in april!
thanks again! sometimes my head gets all messed up with so much stuff...i think. test time is around the corner this week!

good luck on the exam.

are you in minnesota?