Respuesta :
Given:
The expression is
[tex]\dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}[/tex]
To find:
The expressions which are equivalent to the given expression.
Solution:
We have,
[tex]\dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}=\dfrac{1}{5^4}[/tex]
[tex]\dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}=5^{-4}[/tex]
In option A,
[tex](5^{-2})^2=5^{-2\times 2}[/tex]
[tex](5^{-2})^2=5^{-4}[/tex]
This expression is equivalent to the given expression.
In option B,
[tex](5^{-4})^0=5^{-4\times 0}[/tex]
[tex](5^{-4})^0=5^{0}\neq 5^{-4}[/tex]
This expression is not equivalent to the given expression.
Option C,
[tex]\dfrac{5^1}{5^4}=5^{1-4}[/tex]
[tex]\dfrac{5^1}{5^4}=5^{-3}\neq 5^{-4}[/tex]
This expression is not equivalent to the given expression.
Option D,
[tex]5^2\cdot 5^{-6}=5^{2-6}[/tex]
[tex]5^2\cdot 5^{-6}=5^{-4}[/tex]
This expression is equivalent to the given expression.
Therefore, the correct options are A and D.
