Use the laws of exponents to express 9-3/2 · 82/3 as a simple fraction. Show the steps in the simplification

4/27

Step-by-step explanation:

The laws of exponent are used for the simplification of expressions with exponential powers. Considering the given expression, the applicable laws of exponents are

a^-x = (1/a) ^x

and

a^ (x/b) = b√a^x

Hence

9-3/2 · 82/3

= (1/9) ^3/2. 8^2/3

= √ (1/9) ³. ∛8²

= (1/3) ³. 2²

= 1/27. 4

= 4/27