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How do i add an exponent

 Aug 31, 2014

Best Answer 

 #1
avatar+169 
+5

There are a few general rules:

 

$${{\mathtt{X}}}^{{\mathtt{a}}}{\mathtt{\,\times\,}}{{\mathtt{X}}}^{{\mathtt{b}}} = {{\mathtt{X}}}^{\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)}$$

 

$${\frac{{{\mathtt{X}}}^{{\mathtt{a}}}}{{{\mathtt{x}}}^{{\mathtt{b}}}}} = {{\mathtt{X}}}^{\left({\mathtt{a}}{\mathtt{\,-\,}}{\mathtt{b}}\right)}$$

 

$${{\mathtt{X}}}^{{\mathtt{a}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{X}}}^{{\mathtt{a}}} = {\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{X}}}^{{\mathtt{a}}}$$

 

$${\left({{\mathtt{X}}}^{{\mathtt{a}}}\right)}^{{\mathtt{b}}} = {{\mathtt{X}}}^{{\mathtt{ab}}}$$

 

Example:

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {\left({{\mathtt{3}}}^{{\mathtt{2}}}\right)}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{9}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{9}}}^{{\mathtt{x}}}}{{{\mathtt{9}}}^{{\mathtt{3}}}}}$$

 

$${f}{\left({\mathtt{x}}\right)} = {\mathtt{729}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{x}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{729}}}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{x}}}$$

 

$${f}{\left({\mathtt{x}}\right)} = \left({\mathtt{729}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{729}}}}\right){\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{x}}}$$

 

Something like that?

 Aug 31, 2014
 #1
avatar+169 
+5
Best Answer

There are a few general rules:

 

$${{\mathtt{X}}}^{{\mathtt{a}}}{\mathtt{\,\times\,}}{{\mathtt{X}}}^{{\mathtt{b}}} = {{\mathtt{X}}}^{\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)}$$

 

$${\frac{{{\mathtt{X}}}^{{\mathtt{a}}}}{{{\mathtt{x}}}^{{\mathtt{b}}}}} = {{\mathtt{X}}}^{\left({\mathtt{a}}{\mathtt{\,-\,}}{\mathtt{b}}\right)}$$

 

$${{\mathtt{X}}}^{{\mathtt{a}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{X}}}^{{\mathtt{a}}} = {\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{X}}}^{{\mathtt{a}}}$$

 

$${\left({{\mathtt{X}}}^{{\mathtt{a}}}\right)}^{{\mathtt{b}}} = {{\mathtt{X}}}^{{\mathtt{ab}}}$$

 

Example:

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{3}}}^{\left({\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {\left({{\mathtt{3}}}^{{\mathtt{2}}}\right)}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}$$

 

$${f}{\left({\mathtt{x}}\right)} = {{\mathtt{9}}}^{{\mathtt{x}}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{9}}}^{{\mathtt{x}}}}{{{\mathtt{9}}}^{{\mathtt{3}}}}}$$

 

$${f}{\left({\mathtt{x}}\right)} = {\mathtt{729}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{x}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{729}}}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{x}}}$$

 

$${f}{\left({\mathtt{x}}\right)} = \left({\mathtt{729}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{729}}}}\right){\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{x}}}$$

 

Something like that?

Honga Aug 31, 2014

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