Which expression is equivalent to start fraction, 4, to the power minus 8 , divided by, 4, to the power minus 7 , end fraction, times, 4, to the power 0 , question mark

Question

4
−7

4
−8

​
×4
0
?
Answer
Multiple Choice Answers
4, to the power minus 14
−1

11
44
00

Answer 1

To simplify the expression \( \frac{4^{-8}}{4^{-7}} \times 4^0 \), we can follow the rules of exponents.

1. Dividing powers with the same base: \[ \frac{a^m}{a^n} = a^{m-n} \] In our case: \[ \frac{4^{-8}}{4^{-7}} = 4^{-8 - (-7)} = 4^{-8 + 7} = 4^{-1} \]

2. Calculating \( 4^0 \): \[ 4^0 = 1 \]

3. Combining the results: Now we have: \[ 4^{-1} \times 4^0 = 4^{-1} \times 1 = 4^{-1} \]

So, the expression simplifies to \( 4^{-1} \).

The equivalent expression from the options provided is: \[ -1 \]

Thus, the answer is \(-1\).