Positive Rational Number as Exponents
Category : 7th Class
Positive Rational Number as Exponents
Let us consider 'a' be a positive rational number and \[x\] (which is \[\frac{m}{n}\]) be a positive rational exponent then it can also be written as \[{{a}^{x\left( i.e.{{a}^{\frac{m}{n}}} \right)}}\]or the root of \[{{a}^{m}}.\]
For example, \[{{4}^{\frac{3}{2}}}={{\left( {{4}^{3}} \right)}^{\frac{1}{2}}}={{\left( 4\times 4\times 4 \right)}^{\frac{1}{2}}}={{\left( 64 \right)}^{\frac{1}{2}}}=8\]
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