Quantity A	Quantity B
\(\frac{{99}^{9}}{{9^{99}}}\)	\(\frac{{11}^{9}}{{9}^{90}}\)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E
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Key Concept: \((b^k)(c^k)=(bc)^k\)

We can also write: \((bc)^k=(b^k)(c^k)\)

Notice that we can rewrite 99 as (9)(11)
So....

GIVEN:
QUANTITY A: \(\frac{99^9}{9^{99}}\)

QUANTITY B: \(\frac{11^9}{9^{90}}\)


Rewrite 99 as (9)(11) to get:
QUANTITY A: \(\frac{[(9)(11)]^9}{9^{99}}=\frac{(9^9)(11^9)}{9^{99}}=\frac{11^9}{9^{90}}\)

QUANTITY B: \(\frac{11^9}{9^{90}}\)


Answer: C

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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