Question

I need help with this

Answer 1

This is a question on indices.

When we divide indices, we are simply subtracting their powers.

$^{}\frac{14x^4y^6}{7x^8y^2}=14x^4y^6\times7x^{-8}y^{-2}$

In multiplying, we subtract the indices on the LHS and add up the indices on the left since we manipulated the division to a multiplication.

Powers of x: we add 4 to -8 to give us -4

Powers of y: we add 6 to -2 to give us 4

All these while dividing 14 by 7 to get 2

Applying, we get:

$\begin{gathered} 14x^4y^6\times7x^{-8}y^{-2}=2x^{(4-8)}y^{(6-2)} \\ =2x^{-4}y^4 \\ \text{Applying same manipulation, we get:} \\ =\frac{2y^4}{x^4} \end{gathered}$

OPTION A