Value of [tex]\dfrac{125^{1/3a}}{25^{1/2b}}[/tex] is [tex]\dfrac{1}{125^{(\frac{1}{ab})}}[/tex] .
Step-by-step explanation:
Here we have , a-b=3 . We need to evaluate : 125^(1/3a)/25^(1/2b) or ,
[tex]\dfrac{125^{1/3a}}{25^{1/2b}}[/tex] . Let's find out:
⇒ [tex]\dfrac{125^{1/3a}}{25^{1/2b}}[/tex]
⇒ [tex]\dfrac{5^3(^{1/3a})}{5^2(^{1/2b})}[/tex]
⇒ [tex]\dfrac{5(^{3/3a})}{5(^{3/2b})}[/tex]
⇒ [tex]5^{(\frac{1}{a}-\frac{1}{b})} = 5^{(\frac{b-a}{ab})}[/tex]
⇒ [tex]5^{(\frac{-3}{ab})}[/tex]
⇒ [tex]\dfrac{1}{125^{(\frac{1}{ab})}}[/tex]
Therefore, Value of [tex]\dfrac{125^{1/3a}}{25^{1/2b}}[/tex] is [tex]\dfrac{1}{125^{(\frac{1}{ab})}}[/tex] .
