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# 30^10/150^5 = ?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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25 Feb 2016, 18:13
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94% (01:20) correct 6% (02:06) wrong based on 211 sessions

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$$\frac{30^{10}}{150^5}=?$$

A. 6^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3

* A solution will be posted in two days.

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 8341 Re: 30^10/150^5 = ? [#permalink] ### Show Tags 25 Feb 2016, 19:11 1 MathRevolution wrote: 30^10 / 150^5=? A. 6^5 B. 5^6 C. 3^6 D. 6^3 E. 15^3 * A solution will be posted in two days. Whenever we see such Qs, get the Q to its basic terms.. $$\frac{30^{10}}{150^5}=\frac{(2*3*5)^{10}}{(2*3*5*5)^5}$$.. $$\frac{(2^{10}*3^{10}*5^{10})}{(2^5*3^5*5^5*5^5)}=2^5*3^5=6^5$$ ans A _________________ GMAT Club Legend Joined: 12 Sep 2015 Posts: 4214 Location: Canada Re: 30^10/150^5 = ? [#permalink] ### Show Tags Updated on: 28 May 2016, 13:51 1 Quote: 30¹⁰/150⁵ = ? A. 6^5 B. 5^6 C. 3^6 D. 6^3 E. 15^3 Another approach: Notice that 30 = (2)(3)(5) And 150 = (2)(3)(5²) So, 30¹⁰/150⁵ = [(2)(3)(5)]¹⁰/[(2)(3)(5²)]⁵ Simplify to get: [(2¹⁰)(3¹⁰)(5¹⁰)]/[(2⁵)(3⁵)(5¹⁰)] Simplify in parts to get: (2⁵)(3⁵) Rewrite to get: 6⁵ Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Originally posted by GMATPrepNow on 25 Feb 2016, 20:13. Last edited by GMATPrepNow on 28 May 2016, 13:51, edited 1 time in total. SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1725 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: 30^10/150^5 = ? [#permalink] ### Show Tags 26 Feb 2016, 00:44 1 Answer = A $$= 6^5$$ $$\frac{30^{10}}{150^5} = \frac{30^5 * 30^5}{30^5 * 5^5} = \frac{30^5}{5^5} = \frac{6^5 * 5^5}{5^5} = 6^5$$ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8425 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: 30^10/150^5 = ? [#permalink] ### Show Tags 28 Feb 2016, 17:47 30^10 / 150^5=? A. 6^5 B. 5^6 C. 3^6 D. 6^3 E. 15^3 -> 30^10 / 150^5=(30^10)/(5^5)(30^5)=(30^5)/(5^5)=(6^5)(5^5)/(5^5)=6^5. Thus, A is the answer. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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08 Jun 2017, 02:29
MathRevolution wrote:
$$30^{10}/150^5=?$$

A. $$6^5$$
B. $$6^{30}$$
C. $$5^{30}$$
D. $$6^{10}$$
E. $$15^{10}$$

$$30^{10}/150^5$$ = $$30^{10}/(30^5*5^5)$$ = $$30^{5}/(5^5)$$ = $$5^5*6^{5}/(5^5)$$ = $$(6^5)$$

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08 Jun 2017, 08:47
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MathRevolution wrote:
$$30^{10}/150^5=?$$

A. $$6^5$$
B. $$6^{30}$$
C. $$5^{30}$$
D. $$6^{10}$$
E. $$15^{10}$$

Another approach:

$$\frac{30^{10}}{150^5}=\frac{(30^5)(30^5)}{(30^5)(5^5)}$$

$$= \frac{(30^5)}{(5^5)}$$

$$= (\frac{30}{5})^5$$

$$= 6^5$$

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08 Jun 2017, 12:03
Since we need to find out the value of $$30^{10}/150^5$$,

there are 5 such sets of $$\frac{30^{2}}{150}$$
Each of these sets would give us a value of 6. Hence we could get a value for the expression $$6^5$$(Option A)
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10 Jun 2017, 08:06
MathRevolution wrote:
$$30^{10}/150^5=?$$

A. $$6^5$$
B. $$6^{30}$$
C. $$5^{30}$$
D. $$6^{10}$$
E. $$15^{10}$$

We can simplify the given expression:

(30^10)/(150^5)

(30^10)/[(30 x 5)^5]

30^10/(30^5 x 5^5)

(30^5)(30^5)/(30^5 x 5^5)

30^5/5^5 = 6^5
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Math Revolution GMAT Instructor
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11 Jun 2017, 18:26
==> You get $$\frac{30^{10}}{150^5}=\frac{30^{10}}{30^55^5}=\frac{30^5}{5^5}=\frac{(30}{5)^5}=6^5.$$

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16 Oct 2019, 02:03
MathRevolution wrote:
$$\frac{30^{10}}{150^5}=?$$

A. 6^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3

* A solution will be posted in two days.

This is how i solved

(3^10 *10 ^10 ) / 3^5 * 50 ^5 can be simplified to

=( 3^10 * 10^10 ) / ( 3^5 * 10^5 * 5^5 )

( 3^10-5 * 10^ 10 -5 ) / 5^5
= ( 3^5 * 10^5 ) / 5^5

- 3^5 * 5^5* 2*5 / 5^5
= 3^5 *2^5 *5^5-5
= 3^5 * 2^5
take Exponent as common

( 3*2)^5 = 6 ^5 ans A
Re: 30^10/150^5 = ?   [#permalink] 16 Oct 2019, 02:03
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