# 8th Class Mathematics Exponents and Power Exponents

## Exponents

Category : 8th Class

### 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 ${{x}^{-n}}=\frac{1}{{{x}^{n}}}$

${{3}^{0}}=1$

${{3}^{1}}=3$

${{3}^{-1}}=\frac{1}{3}$

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