Respuesta :
You can use the fact that when base are same then power are added.
The value of x in the product of powers given is x = -27
What happens when we multiply numbers with same base?
When you multiply numbers with same base, then their powers get added.
For example, if you have a with power b times a with power c, then you will have result as a with power b+c.
[tex]a^b \times a^c = a^{b+c}[/tex]
How to evaluate x?
Simplifying the equation, we get:
[tex]6^9 \times 6^x = 6^{-11 - 7}\\ 6^{9+x} = 6^{-18}\\ \\ \text{Multiplying with \:} {6^{18}}\\ \\ 6^{18} \times 6^{9+x} = 6^{-18} \times 6 ^{18}\\ 6^{27+x} = 6^{0} = 1\\ [/tex]
Since a number raised to power 0 is 1 only when its power is 0, thus we have:
[tex]27+x =0\\ x=-27[/tex]
Thus, the value of x in the product of powers given is -27.
Learn more about exponent and bases here:
https://brainly.com/question/15722035
Answer:
-7
Step-by-step explanation:
(6^9)(6^x) = 6^2
Taking logarithms to the base 6, we have ...
9 + x = 2
x = -7 . . . . . subtract 9
Step-by-step explanation:
