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Write (8a^−3)^−2/3
in simplest form.
To simplify (8a^−3)^−2/3, we first simplify the expression inside the parentheses raised to the exponent -2/3.
Step 1: Apply the exponent -2/3 to the expression inside the parentheses.
(8a^(-3))^(-2/3) = 8^(-2/3) * (a^(-3))^(-2/3)
Step 2: Simplify 8^(-2/3)
8^(-2/3) can be rewritten as (2^3)^(-2/3)
Since (a^m)^n = a^(m*n), we can simplify (2^3)^(-2/3) as 2^(3*(-2/3))
= 2^(-2)
= 1/2^2
= 1/4
Step 3: Simplify (a^(-3))^(-2/3)
Since (a^m)^n = a^(m*n), (a^(-3))^(-2/3) can be simplified as a^(-3*(-2/3))
= a^2
Putting it all together, we have:
(8a^(-3))^(-2/3) = 8^(-2/3) * (a^(-3))^(-2/3)
= 1/4 * a^2
= a^2/4
Therefore, (8a^(-3))^(-2/3) can be simplified to a^2/4.