Write (8a−3)−23 in simplest form + steps please.
To simplify the expression (8a^(-3))^(-2), we can follow these steps:
Step 1: Simplify the expression inside the parentheses.
Inside the parentheses, we have 8a^(-3). We can simplify this by using the rule of negative exponents. The rule states that a^(-n) is equal to 1/a^n. Applying the rule, we get:
8a^(-3) = 8/(a^3)
Step 2: Apply the power rule.
Now that we have simplified the expression inside the parentheses, we need to evaluate the exponent outside the parentheses. The rule states that (a/b)^n = (a^n) / (b^n). Applying this rule, we get:
(8/(a^3))^(-2) = (8^(-2)) / (a^(3 * -2))
Step 3: Simplify the numerator and denominator.
In the numerator, 8^(-2) is equivalent to 1/8^2 or 1/64.
In the denominator, a^(3 * -2) is equivalent to a^(-6) or 1/(a^6).
Step 4: Combine the simplified numerator and denominator.
Now we can combine the simplified numerator and denominator to get our final answer:
(8/(a^3))^(-2) = 1/64a^6
In summary, the expression (8a^(-3))^(-2) simplifies to 1/64a^6.
(8a−3)−23
8a-3-23
8a-26