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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