Which expressions are equivalent to this exponential expression A)1/5B)-2C)5-^1D) 5^1

Answer: [tex]\dfrac{5^4\times 5^{-2}}{5^3}=\dfrac{1}{5}[/tex]A is correct.Step-by-step explanation:Given: [tex]\dfrac{5^4\times 5^{-2}}{5^3}[/tex]We are given a exponential expression and to simplify it. Exponent Law: Product Rule: [tex]a^m\times a^n=a^{m+n}[/tex]Quotient Rule: [tex]a^m\div a^n=a^{m-n}[/tex]Negative Exponent:  [tex]a^{-m}=\dfrac{1}{a^m}[/tex][tex]\Rightarrow \dfrac{5^4\times 5^{-2}}{5^3}[/tex]Using Quotient rule[tex]\Rightarrow 5^{4-3}\times 5^{-2}[/tex][tex]\Rightarrow 5^{1}\times 5^{-2}[/tex]Using Product Rule[tex]\Rightarrow 5^{1-2}[/tex][tex]\Rightarrow 5^{-1}[/tex]Using Negative exponent law[tex]\Rightarrow \dfrac{1}{5}[/tex]Therefore,  [tex]\dfrac{5^4\times 5^{-2}}{5^3}=\dfrac{1}{5}[/tex]