Use the product, quotient, and power rules, as necessary, to simplify the following expression. Write the answer with only positive exponents.
8−2−1
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.
To simplify the expression 8^(-2)^(-1), we can first apply the power rule, which states that for any real number a and integers m and n, if a^m^)^n^, then we raise a to the power of the product of m and n.
Applying this rule, we have:
8^(-2)^(-1) = 8^((-2)(-1))
Next, we multiply the exponents -2 and -1:
(-2)(-1) = 2
So, we have:
8^((-2)(-1)) = 8^2
Finally, we simplify 8^2, which is equal to 64:
8^2 = 64
Therefore, the simplified expression is 64.
To simplify the expression 8^(-2)(-1), we can apply the product rule and the power rule.
First, let's simplify 8^(-2):
Using the power rule, we know that a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent. In this case, 8^(-2) can be written as 1/8^2.
So, 8^(-2) = 1/8^2 = 1/64.
Now, let's simplify 1/64(-1):
Using the product rule, we know that dividing two numbers with the same base is the same as subtracting their exponents. Therefore, 1/64(-1) = 1/(64^1) = 1/64.
Hence, the simplified expression is 1/64.