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:

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

To find which expression is equivalent to the given expression:

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

125 can be written as 5 × 5 × 5 = 5³

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

Using the exponent rule: $\left(a^{m}\right)^{n}=a^{(m n)}$

     $=\frac{5^6}{5^{\frac{12}{3}}}$

     $=\frac{5^6}{5^4}$

Using the exponent rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$

      $=5^{(6-4)}$

      = 5²

      = 25

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

The expression equivalent to the given expression is 25.

Option D is the correct answer.