Use the​ product, quotient, and power​ rules, as​ necessary, to simplify the following expression. Write the answer with only positive exponents.

Question

8−2−1

Answer 1

To simplify the expression 8^(-2)(-1), we can use the power rule, which states that a^(-b) = 1/(a^b).

Applying the power rule, we have:
8^(-2)(-1) = 1/(8^2)(-1)

Now, using the quotient rule which states that a^(-b)/(a^c) = a^(c-b), we can simplify further:
1/(8^2)(-1) = 1/(8^(2-1))

Simplifying the exponent (2-1), we get:
1/(8^1)

And since anything raised to the power of 1 is itself, we have:
1/8

Therefore, the simplified expression of 8^(-2)(-1) is 1/8.