Answer :
We are given the following two expressions
[tex]5^8\cdot5^2\quad and\quad \frac{5^{20}}{5^2}[/tex]Let us simply both expressions.
For the 1st expression, recall the product rule of exponents given by
[tex]a^x\cdot a^y=a^{x+y}[/tex]Applying the above rule to the 1st expression
[tex]5^8\cdot5^2=5^{8+2}=5^{10}[/tex]For the 2nd expression, recall the quotient rule of exponents given by
[tex]\frac{a^x}{a^y}=a^{x-y}[/tex]Applying the above rule to the 2nd expression
[tex]\frac{5^{20}}{5^2}=5^{20-2}=5^{18}[/tex]As you can see, both expressions are not equivalent.
Therefore, the correct answer is option C
[tex]5^8\cdot5^2=5^{10}\quad and\quad \frac{5^{20}}{5^2}=5^{18}[/tex]