# 7th Class Mathematics Exponents and Power Law of Exponents

## Law of Exponents

Category : 7th Class

### Law of Exponents

For any two rational numbers a and b and for any integer's m and n we have:

• ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$
• $\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}$
• ${{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}={{\left( {{a}^{n}} \right)}^{m}}$
• ${{\left( ab \right)}^{n}}={{a}^{n}}{{b}^{n}}$
• ${{\left( \frac{a}{b} \right)}^{n}}=\frac{{{a}^{n}}}{{{b}^{n}}}$
• If $x$ is a rational number $\left( x>0 \right)$ and a, b are rational exponents so that, a > b then ${{x}^{a}}\div {{x}^{b}}={{x}^{a-b}}.$
• If x is a rational number $\left( x>0 \right)$ and a, b are rational exponents so that $a<b$ then ${{x}^{a}}\div {{x}^{b}}=\frac{1}{{{x}^{b-a}}}.$
• If x is a rational number $(x>0)$ and a, b and c are rational exponents then${{\left\{ {{\left( {{x}^{a}} \right)}^{b}} \right\}}^{c}}={{x}^{abc}}$
• If $x$ and y are rational numbers so that $x>0,\text{ }y>0,$and a is a rational exponent then ${{x}^{a}}\times {{y}^{a}}={{\left( x\times y \right)}^{a}}.$

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