Question

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

Answer 1

125

Explanation:

`\frac{125^{(1)/(3)a}}{25^{(1)/(2)b}} =`

`= \frac{(5^3)^{(1)/(3)a}}{(5^2)^{(1)/(2)b}}`

`= \frac{5^{3 * (1)/(3)a} }{5^{2 * (1)/(2)b}}`

`= \frac{5^{(3)/(3)a}}{5^{(2)/(2)b}}`

`= (5^a)/(5^b)`

`= 5^(a - b)`

`= 5^3`

`= 125`

Answer 2

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

Explanation:

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

`(125^(1/3a))/(25^(1/2b))` . Let's find out:

⇒
`(125^(1/3a))/(25^(1/2b))`

⇒
`(5^3(^(1/3a)))/(5^2(^(1/2b)))`

⇒
`(5(^(3/3a)))/(5(^(3/2b)))`

⇒
`5^{((1)/(a)-(1)/(b))} = 5^{((b-a)/(ab))}`

⇒
`5^{((-3)/(ab))}`

⇒
`\frac{1}{125^{((1)/(ab))}}`

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