Simplify.

(27a^(-6) )^(-2/3)

I got 1/(9a^4 )as my answer, but can someone again please check this. I will appreciate it. I am just unsure if it is correct or not.

The type of math is still Rational Exponents, if any of you have noticed. It is the same as type of math in Simplify, and Simplify 2. Please answer this question/problem as soon as possible. I will still appreciate it.

I would have answered (a^4)/9

Thank you, I think I know what I did wrong. I know it has been a couple days, I haven't been online for those days. Again, thank you.

To simplify the expression (27a^(-6))^(-2/3), we need to follow these steps:

Step 1: Simplify the base
To simplify the base, we can take the cube root of 27, which is 3, and then raise it to the power of -2 or multiply it by -2.

(27a^(-6))^(-2/3) = (3^3 * a^(-6))^(-2/3) = (3^-2 * a^(-6))^(-2/3) = (1/3^2 * a^(-6))^(-2/3) = (1/9 * a^(-6))^(-2/3)

Step 2: Simplify the exponent
To simplify the exponent, we will multiply the exponent outside the parentheses with each exponent inside the parentheses.

(1/9 * a^(-6))^(-2/3) = 1/9^(-2/3) * a^(-6 * -2/3)

Step 3: Simplify the bases with negative exponents
To simplify the base with the negative exponent, we can move it to the numerator and change the sign of the exponent:

1/9^(-2/3) * a^(-6 * -2/3) = 1/(9^(2/3)) * a^(4/3)

Step 4: Simplify the remaining expression
To simplify further, we can evaluate 9^(2/3) as the cube root of 9 squared, which is 3^2 = 9. And for a^(4/3), we can keep it as it is.

1/(9^(2/3)) * a^(4/3) = 1/9 * a^(4/3)

Therefore, the simplified expression is 1/9 * a^(4/3).

The answer you provided, 1/(9a^4), is not correct. The correct simplification is 1/9 * a^(4/3).