Question

Simplify. Assume that no denominator is equal to zero.

Answer 1

Answer: FIRST OPTION.

Step-by-step explanation:

For this exercise it is important to remember a property called "Quotient of Powers property".

 By definition the Quotient of Powers property states the following:

$\frac{a^m}{a^n}=a^{(m-n)}$

You can observe the division of $a^m$ and $a^n$. Since both have the same base "a" , you must rewrite the base and subtract the exponents "m" and "n".

In this case, you have the following expression given in the exercise:

$\frac{4^{12}}{4^{5}}$

Then, you need to apply the Quotient of Powers property rewriting the base 4 and subtracting the exponents 12 and 5.

Therefore, you get the following result:

$=4^{(12-5)}=4^7$

You can notice that it matches with the first option.