The image you provided includes two distinct parts:

1. Top part (a): The equation reads: $6 \times 16 \left( 64 - 1 \right) - 6$ This is a straightforward expression that requires simplification.

2. Bottom part (b): The given expression seems to be: $\frac{2^{n-1} - 2^{n+1}}{3}$ You also attempted some handwritten calculations, but it's unclear from the scribbles. However, I can proceed to solve the expression step by step.

Step-by-step Solutions:

(a) Simplification:

$6 \times 16 (64 - 1) - 6 = 6 \times 16 \times 63 - 6$ Let's break it down: $6 \times 16 = 96$ $96 \times 63 = 6048$ $6048 - 6 = 6042$ Thus, the result is $6042$.

(b) Simplification:

$\frac{2^{n-1} - 2^{n+1}}{3}$ Factor out the common term $2^{n-1}$: $= \frac{2^{n-1}(1 - 2^2)}{3}$ $= \frac{2^{n-1}(1 - 4)}{3}$ $= \frac{2^{n-1} \times (-3)}{3}$ The $-3$ and $3$ cancel out: $= -2^{n-1}$ So, the simplified result is $-2^{n-1}$.

Would you like any further details or clarifications on this?

Here are 5 related questions you can explore:

1. How does factoring out a common term simplify expressions?
2. Can you explain how powers of 2 behave when simplified?
3. What is the significance of negative exponents in expressions?
4. How do you handle more complex algebraic expressions involving exponentials?
5. What is the next step after simplifying an expression?

Tip: When simplifying expressions involving exponents, always check for common factors to streamline the process.