The value of (4/5)^(1/10) is closest to which of the following?

Question

The value of  (\frac{4}{5})^{(\frac{1}{10})}  is closest to which of the following?

A. 1
B. 1/2
C. 0
D. –1/2
E. –1

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Dereno · Accepted Answer

(\frac{4}{5})^{(\frac{1}{10})}

(4/5)^0.1

Any number to the power of zero , equals 1.

0.1 can be considered as close to 0.

So, the equation becomes: (4/5)^0

= 1

Option A

007Phoenix007 · Answer

The number (4/5) is less than 1 and also the power is less than 1.
So, when a number slightly less than 1 raised to a number less than 1, it's approx value comes to 1 
So the option A is correct.

ExpertsGlobal5 · Answer

Explanation:

(4/5)^(1/10) = (0.8)^(1/10)

For any number between 0 and 1, taking the square root results in a larger number than the original.

As you continue to take higher-degree roots (cube root, fourth root, etc.), the result increases, progressively approaching 1.

Note: with higher-degree roots, the value would keep approaching but will always remain less than 1.

A is the correct answer choice.

Shubhradeep · Answer

I went with a more mathematical way

We have 4/5^1/10

let us take log and say
log 4/5^1/10 = y  ( This means 10^y = 4/5^1/10)

1/10 log 4/5 = y

We want to calculate y

let us do some manipulation:

1/10 log 8/10 = 1/10 (log 8 - 1) = 1/10 (3 log 2 - 1)
= 1/10 (3 * 0.3 - 1) = 1/10 (-0.1) = -1/100 ( I remember the values of log 2 , log 3, log 7; useful)

so we have y = -1/100

so 4/5^1/10 = 10 ^ (-1/100)

which is 1/10^(1/100)

very close to 1

Option A

The value of (4/5)^(1/10) is closest to which of the following?

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GMAT Problem Solving (PS) Questions

The value of (4/5)^(1/10) is closest to which of the following?

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