Question

Which expression is equivalent to 4/4^28
4^29
2^27/8^27
4^7 times 4^4
4^28

Answer 1

To simplify the expression \( \frac{4}{4^{28}} \), we can rewrite it as follows:

\[
\frac{4}{4^{28}} = 4^{1 - 28} = 4^{-27}
\]

Now let's check which of the given expressions is equivalent to \( 4^{-27} \).

1. **For \( 4^{29} \)**:
\[
4^{29} \text{ is not equivalent to } 4^{-27}
\]

2. **For \( \frac{2^{27}}{8^{27}} \)**:
We can express \( 8 \) as \( 2^3 \):
\[
\frac{2^{27}}{8^{27}} = \frac{2^{27}}{(2^3)^{27}} = \frac{2^{27}}{2^{81}} = 2^{27 - 81} = 2^{-54}
\]
This is not equivalent to \( 4^{-27} \).

3. **For \( 4^7 \times 4^4 \)**:
Using the property of exponents, we have:
\[
4^7 \times 4^4 = 4^{7 + 4} = 4^{11}
\]
This is not equivalent to \( 4^{-27} \).

4. **For \( 4^{28} \)**:
\[
4^{28} \text{ is not equivalent to } 4^{-27}
\]

Since none of the given options simplify to \( 4^{-27} \), let's consider the possibility of \( 4^{-27} \) being expressed differently. We note that:
- \( 4^{-27} = \frac{1}{4^{27}} \)
- None of the expressions provided were equivalent to this.

Thus, the answer is that there is no expression among the options given that is equivalent to \( \frac{4}{4^{28}} \) or \( 4^{-27} \). If you are looking for something specific or have any requests for further simplifications, let me know!