Question

Select all terms that are equivalent to 4^3/4^5


Show your work.

(2 points)
Responses

1/4^2

4^2

4^−2

1/16

−4^2

Answer 1

To simplify the expression \( \frac{4^3}{4^5} \), we can use the property of exponents that states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Applying this property here:

\[
\frac{4^3}{4^5} = 4^{3-5} = 4^{-2}
\]

Now let's write down the equivalent terms from the given responses:

1. \( \frac{1}{4^2} \): This is equivalent because \( 4^{-2} = \frac{1}{4^2} \).
2. \( 4^2 \): Not equivalent because \( 4^{-2} \) is not equal to \( 4^2 \).
3. \( 4^{-2} \): This is exactly equivalent to the simplified expression.
4. \( \frac{1}{16} \): This is equivalent because \( 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \) since \( 4^2 = 16 \).
5. \( -4^2 \): Not equivalent because \( -4^2 \) equals \(-16\), which is not equal to \( 4^{-2} \).

So the equivalent terms to \( \frac{4^3}{4^5} \) are:

- \( \frac{1}{4^2} \)
- \( 4^{-2} \)
- \( \frac{1}{16} \)

Therefore, the responses that are equivalent to \( \frac{4^3}{4^5} \) are \( \frac{1}{4^2} \), \( 4^{-2} \), and \( \frac{1}{16} \).