Question

Instructions: Select the correct answer from the drop-down menu.
7^16/7^12 = 7^-18/?
The missing term in the denominator is?
A.) 7^-6
B.) 7^-14
C.) 7^-22
D.) 7^22

Answer 1

remember
(x^m)/(x^n)=x^(m-n)

7^16/6^12=7^(16-12)=6=7^4

so

7^4=7^-18/?
?=7^?

7^4=7^-18/7^?
7^-18/7^?=7^(-18-?)=7^4
-18-?=4
add 18
-?=22
tmes -1
?=-22
7^-22

answer is C

Answer 2

Answer:

$7^{-22}$

C is correct.

Step-by-step explanation:

Given: $\dfrac{7^{16}}{7^{12}}=\dfrac{7^{-18}{x}$

using exponent law:

Product Rule: $x^m\times x^n=x^{m+n}$

If base is same in multiply add their exponent.

$\dfrac{7^{16}}{7^{12}}=\dfrac{7^{-18}{x}$

$x=\dfrac{7^{-18}\cdot 7^{12}}{7^{16}}$

$x=7^{-18+12-16}$

$x=7^{-22}$

Hence, At the place of ? is $7^{-22}$