Which expression is equivalent to start fraction, 6, to the power minus 4 , divided by, 6, to the power minus 1 , end fraction, question mark

Question

6
−1

6
−4

​
?
Answer
Multiple Choice Answers
6, to the power 56
5

6, to the power minus 46
−4

6, to the power minus 36
−3

6, to the power 46
4

Answer 1

To simplify the expression \(\frac{6^{-4}}{6^{-1}}\), you can use the properties of exponents. According to the division rule for exponents:

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

Applying this rule to the given expression:

\[ \frac{6^{-4}}{6^{-1}} = 6^{-4 - (-1)} = 6^{-4 + 1} = 6^{-3} \]

So the equivalent expression is:

\[ 6^{-3} \]

Now, let's look at the multiple choice answers provided:

1. \(6^{5}\)
2. \(6^{-4}\)
3. \(6^{-3}\)
4. \(6^{4}\)

The correct answer is:

\(6^{-3}\)