Question

A and b are positive integers and a–b = 3. Evaluate the following: 125^(1/3a)/25^(1/2b)

Answer 1

Answer:

125

Step-by-step explanation:

$\dfrac{125^{\frac{1}{3}a}}{25^{\frac{1}{2}b}} =$

$= \dfrac{(5^3)^{\frac{1}{3}a}}{(5^2)^{\frac{1}{2}b}}$

$= \dfrac{5^{3 \times \frac{1}{3}a} }{5^{2 \times \frac{1}{2}b}}$

$= \dfrac{5^{\frac{3}{3}a}}{5^{\frac{2}{2}b}}$

$= \dfrac{5^a}{5^b}$

$= 5^{a - b}$

$= 5^3$

$= 125$

Answer 2

Value of $\dfrac{125^{1/3a}}{25^{1/2b}}$ is  $\dfrac{1}{125^{(\frac{1}{ab})}}$ .

Step-by-step explanation:

Here we have , a-b=3 . We need to evaluate : 125^(1/3a)/25^(1/2b) or ,

$\dfrac{125^{1/3a}}{25^{1/2b}}$ . Let's find out:

⇒ $\dfrac{125^{1/3a}}{25^{1/2b}}$

⇒ $\dfrac{5^3(^{1/3a})}{5^2(^{1/2b})}$

⇒ $\dfrac{5(^{3/3a})}{5(^{3/2b})}$

⇒ $5^{(\frac{1}{a}-\frac{1}{b})} = 5^{(\frac{b-a}{ab})}$

⇒ $5^{(\frac{-3}{ab})}$

⇒ $\dfrac{1}{125^{(\frac{1}{ab})}}$

Therefore, Value of $\dfrac{125^{1/3a}}{25^{1/2b}}$ is  $\dfrac{1}{125^{(\frac{1}{ab})}}$ .