Question

What inverse operation would be used to solve this problem?
x9 = 3

Answer 1

subtraction, multiplication, division or addition.

Answer 2

To solve the equation \( x^9 = 3 \), you would use the inverse operation of exponentiation, which is taking the root. Specifically, you would take the ninth root of both sides of the equation.

The solution can be written as:

\[
x = 3^{\frac{1}{9}}
\]

So, the inverse operation used here is taking the ninth root.

Answer 3

To solve the equation \( x^9 = 3 \) using one of the four operations you mentioned (subtraction, multiplication, division, or addition), none of those directly applies for the majority of the operations. The best approach in this case is to discuss the operation that could be viewed as 'undoing' the equation, which is exponentiation's inverse, as mentioned before.

However, if you wanted to manipulate a simple algebraic expression involving the variable \( x \) and consider only the operations you mentioned, you might be looking for ways to isolate \( x \) in another context. But for the equation \( x^9 = 3 \), you must use exponentiation's inverse (taking the ninth root), and those four operations do not directly allow solving it.

Thus, it's important to note that none of subtraction, multiplication, division, or addition will directly isolate \( x \) in the case of exponentiation like \( x^9 = 3\).