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# 99^9/9^99 or 11^9/9^90

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99^9/9^99 or 11^9/9^90 [#permalink]  22 Aug 2018, 09:19
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Question Stats:

74% (00:31) correct 25% (00:43) wrong based on 104 sessions
 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
[Reveal] Spoiler: OA

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Re: 99^9/9^99 or 11^9/9^90 [#permalink]  22 Aug 2018, 10:07
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A very Smart Question Rather :

To solve or Compare the two Quantities we will try to get the Fraction ( In particular the Denominator Same for both Qty )

For Qty A we have the Following Situation :

99^ 9 / 9 ^ 99 = ( 11 * 9 ) ^ 9 / 9 ^99 --> 9^9(11^9)/ 9 ^ 99 --> 11^9 / 9 ^ 90 [ We divided or Took 9^ 9 out as Common ] .

So Both Qty are equal

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Re: 99^9/9^99 or 11^9/9^90 [#permalink]  08 Jun 2019, 08:06
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Expert's post
Carcass wrote:
 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

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: $$\frac{11^9}{9^{90}}$$

Cheers,
Brent
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Re: 99^9/9^99 or 11^9/9^90   [#permalink] 08 Jun 2019, 08:06
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