Question

write each side of the equation as a single power.then write and solve an equation to find the value of n. show your work. 23^8.23n=23^5

Answer 1

`\huge \boxed{n=-3}`

Explanation:

`23^(8) * 23^(n)=23^(5)`

`\sf Apply \ rule : a^b * a^c=a^(b+c)`

`23^(8+n)=23^(5)`

`\sf Apply \ rule : a^b=a^c \rightarrow b=c`

`8+n=5`

`\sf Subtract \ 8 \ from \ both \ sides.`

`8+n-8=5-8`

`n=-3`

Answer 2

`23^(n + 8) = 23^5`.

n = -3.

Explanation:

`23^8 * 23^n = 23^5`

`23^(n + 8) = 23^5`

Since both sides have the same base (23), we can solve for n.

n + 8 = 5

n = 5 - 8

n = -3.

Hope this helps!