Answer:
B, C, D
Step-by-step explanation:
One of the rules of exponents is that an exponent in the numerator is equivalent to the opposite of the same exponent in the denominator. That means ...
[tex]4^{-3}=\dfrac{1}{4^3}\qquad\text{matches C.}[/tex]
Another rule of exponents is that an exponent represents repeated multiplication. If a factor can be written using an exponent, the exponents are effectively multiplied.
[tex]4^{-3}=(2^2)^{-3}=2^{2(-3)}=2^{-6}\qquad\text{matches B.}[/tex]
Of course, that repeated multiplication can be shown explicitly:
[tex]\dfrac{1}{4^3}=\dfrac{1}{4}\cdot\dfrac{1}{4}\cdot\dfrac{1}{4}\qquad\text{matches D.}[/tex]
The equivalent expressions to 4^(-3) are B, C, D.
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Additional comment
The expression of G evaluates to ...
[tex]\dfrac{8^{-1}}{2^2}=(2^3)^{-1}\cdot2^{-2}=2^{3(-1)-2}=2^{-5}\qquad\text{not equivalent}[/tex]
