8th Class Mathematics Exponents and Power Exponents

         Exponents

Any number of the form \[{{a}^{n}}\], where n is a natural number and "a" is a real number is called the exponents. Here n is called the power of the number a. Power may be positive or negative.

For any rational number \[{{\left( \frac{a}{b} \right)}^{n}}\], n is the power of the rational number.

\[{{\left( \frac{a}{b} \right)}^{n}}={{\left( \frac{a}{b} \right)}^{n}}=\frac{a}{b}\times \frac{a}{b}\times \frac{a}{b}\times \frac{a}{b}\times \frac{a}{b}\times ----\times \frac{a}{b}\] (n-times)\[=\frac{{{a}^{n}}}{{{b}^{n}}}\]  

\[{{x}^{n}}=x\times x\times x\times x\times ---\times x\](n-times) and

\[{{x}^{-n}}=\frac{1}{x\times x\times x\times x\times x\times ---\times x}\]

Also, \[{{x}^{0}}=1;\] \[{{x}^{1}}=x;\] \[{{x}^{-1}}=\frac{1}{x}\] and \[{{x}^{-n}}=\frac{1}{{{x}^{n}}}\]  

\[{{3}^{0}}=1\]

\[{{3}^{1}}=3\]

\[{{3}^{-1}}=\frac{1}{3}\]