Question

In the equation shown, what is the value of n? 9^7/9^n=9^2

Answer 1

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Explanation:

Answer 2

the value of n for the equation
`(9^(7) )/(9^(n) ) = 9^(2)` is 5

To find the value of n in the equation
`(9^(7) )/(9^(n) ) = 9^(2)`

Using the law of indices for division which states that;

`(a^(m) )/(a^(n) )` =
`a^(m-n)`

Where
`(9^(7) )/(9^(n) ) = 9^(2)`

=
`9^(7-n) =9^(2)`

since the bases are the same, setting the exponents equal to each other:

7 - n = 2

Subtract 2 from both sides

-n = 2 - 7

-n = -5

divides through by -1

-n/-1 = -5/-1

n = 5

Therefore, the value of n for the equation is 5