Option D:
The expression equivalent to the given expression is 25.
Solution:
The image of the question is attached below.
Given expression:
[tex]$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)[/tex]
To find which expression is equivalent to the given expression:
[tex]$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)[/tex]
125 can be written as 5 × 5 × 5 = 5³
[tex]$=\frac{(5^3)^{2}}{(5^3)^{\frac{4}{3}}}[/tex]
Using the exponent rule: [tex]\left(a^{m}\right)^{n}=a^{(m n)}[/tex]
[tex]$=\frac{5^6}{5^{\frac{12}{3}}}[/tex]
[tex]$=\frac{5^6}{5^4}[/tex]
Using the exponent rule: [tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
[tex]=5^{(6-4)}[/tex]
= 5²
= 25
[tex]$\left(\frac{125^{2}}{125^{\frac{4}{3}}}\right)=25[/tex]
The expression equivalent to the given expression is 25.
Option D is the correct answer.
