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write a power represented with a positive base and a positive exponent whose value is less than the base

Sagot :

You mean situation, when  a^b < a. 
There are two ways:
[tex]a^b < a^1 \\ b<1 [/tex]
But exponent function a^b has to be increasing so a>1 
So first solution:  a>1 and 0<b<1.  Examples:
[tex]5^{\frac{1}{2}} < 5 \\ 120^{\frac{1}{12}} < 120[/tex]

and second way:
[tex]a^b < a^1 \\ b>1[/tex]
Exponent function a^b has to be decreasing, so  0<a<1  
Second solution:  a<1 and b>1. Examples:
[tex]\left(\dfrac{1}{2}\right)^{12} < \dfrac{1}{2} \\ \\ \left(\dfrac{12}{39}\right)^{16\frac{1}{2}} < \dfrac{12}{39}[/tex]
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