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Write (8a^−3)^−23
in simplest form.
To simplify the expression (8a^(-3))^(-23), we can start by simplifying the base first:
The base is 8a^(-3). Since we have a negative exponent, we can rewrite it as 1/(8a^3).
Now, let's simplify the exponent:
The exponent is -23. When an expression is raised to a negative exponent, we can rewrite it as the reciprocal of the expression raised to the positive exponent.
So, (1/(8a^3))^(-23) is equivalent to (8a^3)^23.
Next, we can simplify the expression (8a^3)^23.
To do this, we need to apply the power of a power rule, which states that (a^m)^n is equal to a^(m*n).
So, (8a^3)^23 is equivalent to 8^(23)*a^(3*23).
8^(23) is equal to 8 raised to the power of 23, which is a large number.
a^(3*23) is equal to a^(69).
Therefore, the simplified expression is 8^(23)*a^(69).
Note that this is the final answer in simplest form, as there are no more common factors that can be simplified.