Laws of exponent for real numbers

Given below are important laws for math operation of real numbers with exponents.

All the formulas are important as they help us to solve questions so make sure you practice it on your own.

\mathtt{( i) \ a^{m} \times a^{n} =\ a^{m+n}}\\\ \\ \mathtt{( ii) \ \left( a^{m}\right)^{n} =\ a^{m\times n}}\\\ \\ \mathtt{( iii)\frac{a^{m}}{a^{n}} =a^{m-n}}\\\ \\ \mathtt{( iv) \ a^{m} .b^{m} =( ab)^{m}}\\\ \\ \mathtt{( v) \ a^{-m} =\frac{1}{a^{m}}}\\\ \\ \mathtt{( vi) \ \sqrt{ab} =\sqrt{a} .\sqrt{b}}\\\ \\ \mathtt{( vii) \ \sqrt{\frac{a}{b}} =\frac{\sqrt{a}}{\sqrt{b}}}\\\ \\ \mathtt{( viii) \ \left(\sqrt{a} +\sqrt{b}\right)^{2} =a+b+2\sqrt{ab}}

If you want to understand exponents in detail, click the red link.

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