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# (x^25)(y^25) is equivalent to which of the following

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Math Expert
Joined: 02 Sep 2009
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(x^25)(y^25) is equivalent to which of the following [#permalink]

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05 Sep 2017, 00:14
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$$(x^{25})(y^{25})$$ is equivalent to which of the following

A. $$x^{25} + y^{25}$$

B. $$(x + y)^{25}$$

C. $$(x^5y^4)^4(x^5y^9)$$

D. $$(x^5y^4)^4(x^5y^{21})$$

E. $$(x^5y^5)(x^5y^5)$$
[Reveal] Spoiler: OA

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(x^25)(y^25) is equivalent to which of the following [#permalink]

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05 Sep 2017, 00:25
The formula we need to know to solve this question :
$$(a^m)^n = a^{m*n}$$
$$a^m * a^n = a^{m+n}$$

Taking these rules in mind, we can evaluate the answer options and find out
which of the answer option yields the expression $$(x^{25}*y^{25})$$.

$$(x^5*y^4)^4(x^5*y^9)$$ = $$(x^{5*4}y^{4*4})(x^5*y^9)$$ = $$(x^{20 + 5}*y^{16 + 9})$$ = $$(x^{25}*y^{25})$$
Hence, Option C is our answer!
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Re: (x^25)(y^25) is equivalent to which of the following [#permalink]

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07 Sep 2017, 15:47
Bunuel wrote:
$$(x^{25})(y^{25})$$ is equivalent to which of the following

A. $$x^{25} + y^{25}$$

B. $$(x + y)^{25}$$

C. $$(x^5y^4)^4(x^5y^9)$$

D. $$(x^5y^4)^4(x^5y^{21})$$

E. $$(x^5y^5)(x^5y^5)$$

Looking at our answer choices, we see that answer C is correct:

[(x^5)(y^4)]^4 * (x^5)(y^9)

[(x^20)(y^16)] * (x^5)(y^9) = x^25 * y^25

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Re: (x^25)(y^25) is equivalent to which of the following   [#permalink] 07 Sep 2017, 15:47
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