Answer: Last option.
Step-by-step explanation:
To find which expression in equivalent to the expression [tex]\frac{125^2}{125^\frac{4}{3} }[/tex], you need to remember :
The Power of a power property:
[tex](a^m)^n=a^{(mn)}[/tex]
The Quotient of powers property:
[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]
And the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Knowing that:
[tex]125=5*5*5=5^3[/tex]
Then, you get:
[tex]\frac{125^2}{125^\frac{4}{3} }=\frac{(5^3)^2}{(5^3)^\frac{4}{3} }=\frac{5^6}{5^4}=5^{(6-4)}=5^2=25[/tex]
