# 7th Class Mathematics Exponents and Power Positive Rational Number as Exponents

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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