Question

I need help with my math

Answer 1

From the question, we can deduce the answer using indices which deals with power of numbers, e.g

`(5^2.5^3)/(5^4)=(5^(2+3))/(5^4)=(5^5)/(5^4)=5^(5-4)=5^1=5`

Also, for the next one,

`(9^4.9^6)/(9^8)=(9^(4+6))/(9^8)=(9^(10))/(9^8)=9^(10-8)=9^2`

This applies to every other ones provided in the question,

Considering Option D,

`\begin{gathered} (b^(2k).b^(3k))/(b^(4k)) \\ \text{where k is 2,} \\ (b^(2(2)).b^(3(2)))/(b^(4(2)))=\text{ }(b^4.b^6)/(b^8)=(b^(4+6))/(b^8)=(b^(10))/(b^8)=b^(10-8)=b^2 \\ \text{Where k=2, Option D is favoured} \end{gathered}`

Since the equation D favours the solution,

Hence, the best option is D.