Question

3. Which of the following is equivalent to the expression 44 x 4-67оа142Ob1410Ос410Od42ОeDon't Know

Answer 1

To solve the exercise you can use these rules of exponents

$\begin{gathered} a^m\cdot a^n=a^{m+n} \\ \text{and} \\ a^{-m}=\frac{1}{m} \end{gathered}$

So, in this case, you have

Using the first rule

$4^4\cdot4^{-6}=4^{4-6}=4^{-2}$

Using the second rule

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

Then,

$4^4\cdot4^{-6}=\frac{1}{4^2}$

Therefore, the expression equivalent to the given expression is

$\frac{1}{4^2}$

and the correct answer is option a.