If (1/50)^a(1/20)^4 = 1/50 (100)^-6 , a = ?

Question

If  (\frac{1}{50})^a(\frac{1}{20})^4 = \frac{1}{50} (100)^{-6} , a = ?

A. 3
B. 4
C. 5
D. 6
E. 7

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

shivani1351 · Answer

We know:
50 = 5^2 * 2
20 = 2^2 * 5
100 = 2^2 * 5^2

L.H.S. of the equation = (2^-1 * 5^-2)^a * (2^-2 * 5^-1)^4 = 2^-(a+8) * 5^-(2a+4)
R.H.S. of the equation = (2^-1 * 5^-2) * (2^-12 * 5^-12) = 2^-13 * 5^-14

Equating the powers of both sides we get:
a+8 = 13, thus, a = 5
2a+4 = 14, thus, a = 5

Hence, the correct answer is Option C - 5

Hope this helps!

vasu1104 · Answer

{ 1/ (2 * 5)^a }* 1 / (2^2 * 5 )^4 = 1/ (2*5^2) {(5)^2 (2)^2}^6
{1/2^a* 5^2a }* { 1/2^8 * 5^4 } = 1/ 2^13 * 5^14 
1/ 2^a+8 * 5^2a+4 = 1 / 2^13 * 5^14
a+ 8 = 13
a = 5

Dereno · Answer

(\frac{1}{50})^a(\frac{1}{20})^4 = \frac{1}{50} (100)^{-6}

we need to find a?

(50)^-a (20)^-4 = (50)^-1 (100)^-6

(5^2 * 2) ^-a ( 2^2 *5)^-4 = (5^2*2)^-1 .(5^2*2^2)^-6

5^(-2a-4) * 2^(-a-8) = 5^-14 * 2^-13

Equating the powers of 2 or 5, we get

-2a-4 = -14

2a =10. Thus,  a =5

Option C

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=5DTo02vOsTU

Rishm · Answer

I just transformed (100)^-6 into 1/100^6, once u see this results into something which starts with 5, and if you check only option C helps us here where (1/50)^5 gives 25 something, and when you multiply it by 2 as 20 is the base , it gives results in something that starts with 5.

If (1/50)^a(1/20)^4 = 1/50 (100)^-6 , a = ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If (1/50)^a(1/20)^4 = 1/50 (100)^-6 , a = ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards