(8a^-3)^-2/3 In Simplest Form

Jasonbradley

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Jun 16, 2024

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Simplifying (8a^-3)^-2/3

Let's break down how to simplify the expression (8a^-3)^-2/3 step by step:

Applying the Power of a Power Rule

• Rule: (x^m)^n = x^(m*n)

Applying this rule to our expression:

(8a^-3)^-2/3 = 8^(-2/3) * (a^-3)^(-2/3)

Simplifying the Numerical Term

• Rule: x^(-n) = 1/x^n

Simplifying 8^(-2/3):

8^(-2/3) = 1/8^(2/3)

• Rule: x^(m/n) = (n√x)^m

Simplifying 1/8^(2/3):

1/8^(2/3) = 1/(∛8)^2 = 1/2^2 = 1/4

Simplifying the Variable Term

• Rule: (x^m)^n = x^(m*n)

Simplifying (a^-3)^(-2/3):

(a^-3)^(-2/3) = a^(-3)*(-2/3) = a^2

Combining the Simplified Terms

Now we have:

8^(-2/3) * (a^-3)^(-2/3) = (1/4) * a^2

Final Simplified Form

Therefore, the simplified form of (8a^-3)^-2/3 is a^2/4.