Final answer:
To work out the value of n in the expression 2³ x 2²n x 2³ = (2²)³, simplify both sides of the equation and equate the exponents. The value of n is 1/4.
Step-by-step explanation:
To work out the value of n, we can simplify the given expression: 2³ x 2²n x 2³ = (2²)³.
First, solve the left side of the equation: 2³ x 2²n x 2³ = 2³+³ x 2²n = 2⁶ x 2²n = 2⁸n.
Then, simplify the right side of the equation: (2²)³ = 2⁶.
Since both sides are equal, we can equate the exponents: 2⁸n = 2⁶.
Therefore, n = 2⁶ / 2⁸ = 1 / 2² = 1/4.