Simplify: eight to the negative fifth divided by eight to the negative third

Question

Group of answer choices

one divided by the quantity eight squared

one divided by the quantity eight to the eighth power

82

88

Answer 1

To simplify the expression \( \frac{8^{-5}}{8^{-3}} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Now, applying this property:

\[ \frac{8^{-5}}{8^{-3}} = 8^{-5 - (-3)} = 8^{-5 + 3} = 8^{-2} \]

Next, we can express \( 8^{-2} \) as:

\[ 8^{-2} = \frac{1}{8^2} \]

Thus, the simplified result is:

\[ \frac{1}{8^2} \]

So, the correct option from the provided choices is:

• one divided by the quantity eight squared