Option B : ![\frac{1}{\sqrt[3]{x^{5} } }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bx%5E%7B5%7D%20%7D%20%7D)
is the expression equivalent to 
Explanation:
The given expression is
Rewriting the expression using the exponent rule, 
Hence, we get,
Simplifying, we get,
Applying the rule, ![a^{\frac{1}{n}}=\sqrt[n]{a}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Ba%7D)
Thus, we have,
Now, we shall determine from the options that which expression is equivalent to
Option A: ![\frac{1}{\sqrt[5]{x^{3} } }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%20%7D%20%7D)
The expression is not equivalent to simplified expression
Thus, the expression is not equivalent to
Hence, Option A is not the correct answer.
Option B:
The expression is equivalent to the simplified expression
Thus, the expression is equivalent to
Hence, Option B is the correct answer.
Option C: ![-\sqrt[3]{x^5}](https://tex.z-dn.net/?f=-%5Csqrt%5B3%5D%7Bx%5E5%7D)
The expression is not equivalent to the simplified expression
Thus, the expression is not equivalent to
Hence, Option C is not the correct answer.
Option D: ![-\sqrt[5]{x^3}](https://tex.z-dn.net/?f=-%5Csqrt%5B5%5D%7Bx%5E3%7D)
The expression is not equivalent to the simplified expression
Thus, the expression is not equivalent to
Hence, Option D is not the correct answer.
⇒ </em>This function is same as
so its range is <em>( 0 , ∞ )</em>.
⇒ </em>If we double each value of the function
, which has range ( 0 , ∞ ), but still the value of extremes won't change as 0*2=0 and ∞*2=∞. Therefore the range remains as <em>( 0 , ∞ )</em>.
</em> ⇒ If we add 2 to each value of the function
