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]
