Question

If x=0.125,find the value of (1/x)power1/3

Answer 1

(1/x)∧(1/3)
=(1/0.125)∧(1/3)
=[(1×1000)/125]∧(1/3)
=(8)∧(1/3)
=(2³)∧(1/3)
=(2)∧1
=2

Answer 2

If $x=0.125$, then the value of $(\frac{1}{x}) ^{\frac{1}{3} }$ is 2.

Step-by-step Explanation

Given that $x=0.125$

To be found:

To find the value of $(\frac{1}{x}) ^{\frac{1}{3} }$

Solution:

We have $x=0.125$

The p/q form of x is $\frac{125}{1000}$

Now, substituting the value of x in $(\frac{1}{x}) ^{\frac{1}{3} }$, we get

$(\frac{1}{x}) ^{\frac{1}{3} }=(\frac{1}{0.125}) ^{\frac{1}{3} }$    -----(1)

Using the p/q form of x, we get (1) as,

$(\frac{1}{x}) ^{\frac{1}{3} }=(\frac{1}{125/1000}) ^{\frac{1}{3} }\\\implies (\frac{1}{x}) ^{\frac{1}{3} }=(\frac{1000}{125}) ^{\frac{1}{3} }$

Solving, we get

$(\frac{1}{x}) ^{\frac{1}{3} }=(8) ^{\frac{1}{3} }\\\implies (\frac{1}{x}) ^{\frac{1}{3} }=(2^{3} )^{\frac{1}{3} }\\\implies (\frac{1}{x}) ^{\frac{1}{3} }=2$

Therefore, when $x=0.125$, $(\frac{1}{x}) ^{\frac{1}{3} }$ is equal to 2.

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