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30^10/150^5 = ?

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30^10/150^5 = ?  [#permalink]

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New post 25 Feb 2016, 18:13
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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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Re: 30^10/150^5 = ?  [#permalink]

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New post 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
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Re: 30^10/150^5 = ?  [#permalink]

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New post 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

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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.
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Re: 30^10/150^5 = ?  [#permalink]

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New post 26 Feb 2016, 00:44
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Answer = A \(= 6^5\)

\(\frac{30^{10}}{150^5} = \frac{30^5 * 30^5}{30^5 * 5^5} = \frac{30^5}{5^5} = \frac{6^5 * 5^5}{5^5} = 6^5\)
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Re: 30^10/150^5 = ?  [#permalink]

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New post 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.
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Re: 30^10/150^5 = ?  [#permalink]

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New post 08 Jun 2017, 02:29
MathRevolution wrote:
\(30^{10}/150^5=?\)

A. \(6^5\)
B. \(6^{30}\)
C. \(5^{30}\)
D. \(6^{10}\)
E. \(15^{10}\)


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

Answer: Option A
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Re: 30^10/150^5 = ?  [#permalink]

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New post 08 Jun 2017, 08:47
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Top Contributor
MathRevolution wrote:
\(30^{10}/150^5=?\)

A. \(6^5\)
B. \(6^{30}\)
C. \(5^{30}\)
D. \(6^{10}\)
E. \(15^{10}\)


Another approach:

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

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

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

\(= 6^5\)

Answer:

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Re: 30^10/150^5 = ?  [#permalink]

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New post 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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Re: 30^10/150^5 = ?  [#permalink]

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New post 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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Re: 30^10/150^5 = ?  [#permalink]

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New post 11 Jun 2017, 18:26
==> You get \(\frac{30^{10}}{150^5}=\frac{30^{10}}{30^55^5}=\frac{30^5}{5^5}=\frac{(30}{5)^5}=6^5.\)

The answer is A.
Answer: A
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Re: 30^10/150^5 = ?  [#permalink]

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New post 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
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Re: 30^10/150^5 = ?   [#permalink] 16 Oct 2019, 02:03
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