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;

$\begin{gathered} \frac{a^x}{a^y}=a^{x-y} \\ \\ a^x\text{ }\times a^y=a^{x+y} \\ \\ a^{-1\text{ }}\text{ = }\frac{1}{a} \end{gathered}$

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

a) we have;

$\frac{2^4}{2^6\text{ }}=2^{4-6}=2^{-2\text{ }}=\text{ }\frac{1}{2^2}\text{ = }\frac{1}{4}$

b) we have;

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

c) We have;

$(2^5)(2^{-7})=2^{5-7}=2^{-2}\text{ = }\frac{1}{2^2}\text{ = }\frac{1}{4}$

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