If 'slap' times speed equals power, what will be the dimensional equation for 'slap' ?

The correct option is MLT⁻².

To find the dimensional equation for 'slap', we start with the formula given in the question:
$\text{slap}\times \text{speed}=\text{power}$

Rearranging the equation to solve for 'slap':
$\text{slap}=\frac{\text{power}}{\text{speed}}$

Now, let's write the dimensional formulas for the quantities involved:

1. Dimensional formula of speed:
Speed is distance per unit time, so its dimensions are:
$\left[\text{speed}\right]={\text{LT}}^{-1}$

2. Dimensional formula of power:
Power is work done per unit time, which is:
$\text{Power}=\frac{\text{Work}}{\text{Time}}=\frac{\text{Force}\times \text{Displacement}}{\text{Time}}$
The dimensions of force are ${\text{MLT}}^{-2}$, displacement is $\text{L}$, and time is $\text{T}$. Thus:
$\left[\text{power}\right]=\frac{{\text{MLT}}^{-2}\times \text{L}}{\text{T}}={\text{ML}}^2{\text{T}}^{-3}$

Now, we substitute these dimensions into our equation for 'slap':
$\left[\text{slap}\right]=\frac{{\text{ML}}^2{\text{T}}^{-3}}{{\text{LT}}^{-1}}$

Simplifying the exponents:
$\left[\text{slap}\right]={\text{ML}}^{2-1}{\text{T}}^{-3-\left(-1\right)}$
$\left[\text{slap}\right]={\text{MLT}}^{-2}$

Therefore, the dimensional equation for 'slap' is MLT⁻² (which represents force).