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# If xy is not equal to 0, then which of the following is the equivalent

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Math Expert
Joined: 02 Sep 2009
Posts: 43804
If xy is not equal to 0, then which of the following is the equivalent [#permalink]

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04 Sep 2017, 23:46
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Difficulty:

35% (medium)

Question Stats:

71% (01:35) correct 29% (01:19) wrong based on 114 sessions

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If xy is not equal to 0, then which of the following, is the equivalent of $$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$?

A. $$x^6y^2(x + 1)$$

B. $$x^4y^4(x + 1)$$

C. $$2x^4y^4$$

D. $$2x^5y^3$$

E. $$2x^6y^2$$
[Reveal] Spoiler: OA

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Posts: 27
Re: If xy is not equal to 0, then which of the following is the equivalent [#permalink]

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05 Sep 2017, 00:46
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of $$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$?

A. $$x^6y^2(x + 1)$$

B. $$x^4y^4(x + 1)$$

C. $$2x^4y^4$$

D. $$2x^5y^3$$

E. $$2x^6y^2$$

X^5y^3 + x^5y^3 / (y/x)

= x^5y^2(x+1) *x/y
= x^6y^2(x+1)

A should be correct.

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Kshitij
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Re: If xy is not equal to 0, then which of the following is the equivalent [#permalink]

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05 Sep 2017, 07:05
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of $$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$?

A. $$x^6y^2(x + 1)$$

B. $$x^4y^4(x + 1)$$

C. $$2x^4y^4$$

D. $$2x^5y^3$$

E. $$2x^6y^2$$

$$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$

$$\frac{x^6y^3+x^5y^3}{(\frac{y}{x})}$$

$$\frac{x^5y^3(x +1)}{(\frac{y}{x})}$$

$$(x*y^{-1})x^5y^3(x +1)$$

$$x^6y^2(x +1)$$

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Joined: 22 May 2016
Posts: 1329
If xy is not equal to 0, then which of the following is the equivalent [#permalink]

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06 Sep 2017, 12:42
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of $$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$?

A. $$x^6y^2(x + 1)$$

B. $$x^4y^4(x + 1)$$

C. $$2x^4y^4$$

D. $$2x^5y^3$$

E. $$2x^6y^2$$

It took me a long time to figure out that the denominator is $$(\frac{x}{y})^{-1}$$, not $$(\frac{x}{y}) - 1$$

$$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$ =

$$\frac{x^6y^3+x^5y^3}{(\frac{y}{x})}$$ =

$$(\frac{x}{y}) * (x^5y^3)(x + 1)$$ =

$$(x^1y^{-1}) * (x^5y^3)(x + 1)$$=

$$x^{(1+5)}y^{(-1+3)} * (x + 1)$$

$$x^6y^2(x + 1)$$

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Re: If xy is not equal to 0, then which of the following is the equivalent [#permalink]

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07 Sep 2017, 15:41
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of $$\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}$$?

A. $$x^6y^2(x + 1)$$

B. $$x^4y^4(x + 1)$$

C. $$2x^4y^4$$

D. $$2x^5y^3$$

E. $$2x^6y^2$$

Let’s first simplify the numerator of the given expression:

(x^6)(y^3) + (x^5)(y^3)

(x^5)(y^3)(x + 1)

Simplifying the denominator, we have: (x/y)^-1 = y/x

Now we have:

(x^5)(y^3)(x + 1)/(y/x) = (x^5)(y^3)(x + 1)*(x/y) = (x^6)(y^2)(x + 1)

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Re: If xy is not equal to 0, then which of the following is the equivalent   [#permalink] 07 Sep 2017, 15:41
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