The simplest form of the given expression [tex](8a^{-3})^{\frac{-4}{3}}[/tex] is [tex]a^4/16[/tex] and this can be determined by using the arithmetic operations.
Given :
Expression -- [tex](8a^{-3})^{\frac{-4}{3}}[/tex]
The following steps can be used in order to determine the simplest form of the given expression:
Step 1 - The arithmetic operations can be used in order to determine the simplest form of the given expression.
Step 2 - Write the given expression.
[tex]=(8a^{-3})^{\frac{-4}{3}}[/tex]
Step 3 - Split the above expression.
[tex]=8^{\frac{-4}{3}}\times (a^{-3})^{\frac{-4}{3}}[/tex]
Step 4 - Now, 8 can be written as [tex]2^3[/tex] in the above expression.
[tex]=(2^3)^{\frac{-4}{3}}\times (a^{-3})^{\frac{-4}{3}}[/tex]
Step 5 - Simplify the above expression.
[tex]=(2)^{{-4}}\times (a)^{4}[/tex]
Step 6 - Further, simplify the above expression.
[tex]=\dfrac{a^4}{16}[/tex]
For more information, refer to the link given below:
https://brainly.com/question/15385899
