Category : 8th Class
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 \[{{x}^{-n}}=\frac{1}{{{x}^{n}}}\]
\[{{3}^{0}}=1\]
\[{{3}^{1}}=3\]
\[{{3}^{-1}}=\frac{1}{3}\]
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