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# If x = a^5 and y = a^6, a is not equal to 0, which of the following is

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If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

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17 Jul 2018, 23:45
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Difficulty:

15% (low)

Question Stats:

79% (00:56) correct 21% (01:02) wrong based on 43 sessions

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If $$x = a^5$$ and $$y = a^6$$,a is not equal to 0, which of the following is equivalent to $$a^{13}$$?

A. $$xy$$

B. $$x^2 y$$

C. $$\frac{x^3}{y}$$

D. $$\frac{x^4}{y}$$

E. $$\frac{y^3}{x}$$

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Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

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17 Jul 2018, 23:58
Bunuel wrote:
If $$x = a^5$$ and $$y = a^6$$,a is not equal to 0, which of the following is equivalent to $$a^{13}$$?

+1 for E.

x = a^5
y = a^6
a^13 = ?

Now,plug in the values from option i.e 6*3 - 5 = 18 - 5 = 13
y^3 = a^18

and,
y^3 / x
= a^18 / a^5 = a^13

Hence, E.
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Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

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18 Jul 2018, 04:26

Solution

Given:

• $$x=a^5$$
• $$y=a^6$$

To find:

• Among the given options, which is equal to$$a^{13}$$

Approach and Working:

Let’s check every option one by one.

A. $$xy= a^5 * a^6= a^11$$
B. $$x^2y= a^{10}*a^6=a=^{16}$$
C. $$\frac{x^3}{y}= \frac{a^{15}}{a^6}= a^9$$
D. $$\frac{x^4}{y}= \frac{a^{20}}{a^6}= a^{14}$$

Only one option is remaining so that has to be the answer ?
However, let’s calculate it.

E. $$\frac{y^3}{x}= \frac{a^{18}}{a^5}= a^{13}$$

Hence, the correct answer is option E.

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If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

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18 Jul 2018, 07:30
Given that: x = $$a^5$$ and y = $$a^6$$

Common rules in exponents
$$(a^m)^n = a^{m*n}$$ | $$a^m * a^n = a^{m + n}$$ | $$\frac{1}{a^n} = a^{- n}$$

We need to find which of the answer options is equal to a^{13}.

A. $$xy = a^{5+6} = a^{11}$$
B. $$x^2*y = a^{5*2}*a^6 = a^{16}$$
C. $$\frac{x^3}{y} = a^{5*3}*a^{-6} = a^{9}$$
D. $$\frac{x^4}{y} = a^{5*4}*a^{-6} = a^{14}$$

E. $$\frac{y^3}{x} = a^{6*3}*a^{-5} = a^{13}$$ (Option E)
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Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is  [#permalink]

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22 Jul 2018, 17:06
Bunuel wrote:
If $$x = a^5$$ and $$y = a^6$$,a is not equal to 0, which of the following is equivalent to $$a^{13}$$?

A. $$xy$$

B. $$x^2 y$$

C. $$\frac{x^3}{y}$$

D. $$\frac{x^4}{y}$$

E. $$\frac{y^3}{x}$$

Let’s check each given choice:

A) xy

xy = (a^5)(a^6) = a^11

A is not correct.

B) x^2y

x^2y = (a^5)^2(a^6) = (a^10)(a^6) = a^16

B is not correct.

C) x^3/y

x^3/y = (a^5)^3/(a^6) = (a^15)/(a^6) = a^9

C is not correct.

D) x^4/y

x^4/y = (a^5)^4/(a^6) = (a^20)/(a^6) = a^14

D is not correct either. So the right answer must be E, but let’s verify it anyway.

E) y^3/x

y^3/x = (a^6)^3/(a^5) = (a^18)/(a^5) = a^13

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Re: If x = a^5 and y = a^6, a is not equal to 0, which of the following is &nbs [#permalink] 22 Jul 2018, 17:06
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