If (1/125 )^a(1/16)^8 = 1/5 (10)^32, a = ?

Question

If  (\frac{1}{125})^a (\frac{1}{16})^8 = \frac{1}{5 (10)^{32} }  , a = ?

A. -11
B. -5
C. 5
D. 10
E. 11

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shivani1351 · Answer

Hi  ExpertsGlobal5 ,
Can you please re-check the question and the options provided, I feel there's some misprint in the question.
Thanks!

vasu1104 · Answer

Hi, expertglobal5 , there is some problem with the question. with the given stem, a will be in fraction and not an integer. 
please look into it.

thank you in advance.

Bunuel · Answer

Fixed the formatting. Thank you!

shivani1351 · Answer

Hi  Bunuel , thank you for fixing it, it looks good now!

The correct answer should be  Option E :

Let's simplify both - LHS and RHS to find out the value of a:

LHS:

5^(-3a) * 2^(-32)

Similarly,  RHS:

5^(-33) * 2^(-32)

Thus, we are given that: 5^(-3a) * 2^(-32) = 5^(-33) * 2^(-32)

Cancelling off 2^(-32) from both the sides of the equation, we get:

5^(-3a) = 5^(-33)

Thus, -3a = -33

Hence, the value of a = 11 (Option E)

007Phoenix007 · Answer

(1/125)^a * (1/16)^8 = (1/5*(10)^32)
= 5^(-3a) * (2^(-4))^8 = (5^-1*(2*5)^-32
= 5^-3a * 2^-32 = 5^-33 * 2^-32
= -3a= -33
Therefore a= 11
So option E

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=keDO3H_2RSU

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