Question

Which of the following is equivalent to (125^2/ 125^4/3)

Answer 1

Option D:

The expression equivalent to the given expression is 25.

Solution:

The image of the question is attached below.

Given expression:

`$\left(\frac{125^(2)}{125^{(4)/(3)}}\right)`

To find which expression is equivalent to the given expression:

`$\left(\frac{125^(2)}{125^{(4)/(3)}}\right)`

125 can be written as 5 × 5 × 5 = 5³

`$=\frac{(5^3)^(2)}{(5^3)^{(4)/(3)}}`

Using the exponent rule:
`\left(a^(m)\right)^(n)=a^((m n))`

`$=\frac{5^6}{5^{(12)/(3)}}`

`$=(5^6)/(5^4)`

Using the exponent rule:
`(a^(m))/(a^(n))=a^(m-n)`

`=5^((6-4))`

= 5²

= 25

`$\left(\frac{125^(2)}{125^{(4)/(3)}}\right)=25`

The expression equivalent to the given expression is 25.

Option D is the correct answer.