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Rational Exponents Calculator
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Rational Exponents Calculator differ from number exponents. When an expression or number has a number exponent, we multiply the base with itself that many number of times. When they have a rational exponent, say $\frac{1}{n}$, we take the nth root of the base. The denominator in a rational exponent denotes that particular root of the base, whereas the numerator denotes the number of times we have to multiply the base with itself.

For example, 2$^{\frac{2}{3}}$ means that:
  • We have get the 3rd root of two, or, in simple words, we have to get the cube root of 2. (because 3 is the denominator of the rational exponent)
  • Then multiply the cube root of two with itself two times ( because 2 is the numerator of rational exponent)
Conversely, we can also solve it as follows: -
  • Get the square of 2. (because 2 is the numerator of the rational exponent)
  • Then find the cube root of the result (because 3 is the denominator of the rational exponent).
 

Steps for Rational Exponents Calculator

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Step 1 :  

Find the exponent of lowest possible base of the given number x.



Step 2 :  

Apply the formula x(exponent x radical)



Problems on Rational Exponents Calculator

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  1. Evaluate $\sqrt[4]{5^{8}}$


    Step 1 :  

    $\Rightarrow$ $\sqrt[4]{5^{8}}$


    $\Rightarrow$ $(5^{8})^{(\frac{1}{4})}$



    Step 2 :  

    $\Rightarrow$ $(5)^{(8 \times \frac{1}{4})}$


    $\Rightarrow$ $5^{(\frac{8}{4})}$


    $\Rightarrow$ $5^{2}$


    $\Rightarrow$ 25



    Answer  :  

    25



  2. Evaluate $\sqrt[3]{4^{6}}$


    Step 1 :  

    $\Rightarrow$ $\sqrt[3]{4^{6}}$


    $\Rightarrow$ $(4^{6})^{(\frac{1}{3})}$



    Step 2 :  

    $\Rightarrow$ $(4)^{(6 \times \frac{1}{3})}$


    $\Rightarrow$ $4^{(\frac{6}{3})}$


    $\Rightarrow$ $4^{2}$


    $\Rightarrow$ 16



    Answer  :  

    16



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