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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

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

1. Evaluate $\sqrt{5^{8}}$

Step 1 :

$\Rightarrow$ $\sqrt{5^{8}}$

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

Step 2 :

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

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

$\Rightarrow$ $5^{2}$

$\Rightarrow$ 25

25

2. Evaluate $\sqrt{4^{6}}$

Step 1 :

$\Rightarrow$ $\sqrt{4^{6}}$

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

Step 2 :

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

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

$\Rightarrow$ $4^{2}$

$\Rightarrow$ 16