Question

Need help. Two options is right I just don't know

Answer 1

The correct options are A, B and C

Here, we want to select which of the given expressions have the same value as 1/4

Three important laws of indices are needed to get this;

`\begin{gathered} (a^x)/(a^y)=a^(x-y) \\ \\ a^x\text{ }* a^y=a^(x+y) \\ \\ a^{-1\text{ }}\text{ = }(1)/(a) \end{gathered}`

So, with these laws, we can actually proceed to solve the question. Let us consider the options one after the other

a) we have;

`\frac{2^4}{2^6\text{ }}=2^(4-6)=2^{-2\text{ }}=\text{ }(1)/(2^2)\text{ = }(1)/(4)`

b) we have;

`((4^3)(4^2))/((4^2)^3)\text{ = }(4^(3+2))/(4^6)\text{ = }(4^5)/(4^6)=4^(5-6)=4^(-1)\text{ = }(1)/(4)`

c) We have;

`(2^5)(2^(-7))=2^(5-7)=2^(-2)\text{ = }(1)/(2^2)\text{ = }(1)/(4)`

d) We have;

`(4^5)(4^(-3))=4^(5-3)=4^2\text{ = 16}`

As we can see, options A, B and C are correct