Question

Select all the expressions that are equivalent

Answer 1

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 ...

  $4^{-3}=\dfrac{1}{4^3}\qquad\text{matches C.}$

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.

  $4^{-3}=(2^2)^{-3}=2^{2(-3)}=2^{-6}\qquad\text{matches B.}$

Of course, that repeated multiplication can be shown explicitly:

  $\dfrac{1}{4^3}=\dfrac{1}{4}\cdot\dfrac{1}{4}\cdot\dfrac{1}{4}\qquad\text{matches D.}$

The equivalent expressions to 4^(-3) are B, C, D.

_____

Additional comment

The expression of G evaluates to ...

  $\dfrac{8^{-1}}{2^2}=(2^3)^{-1}\cdot2^{-2}=2^{3(-1)-2}=2^{-5}\qquad\text{not equivalent}$