We start with the given equation:

$x^7 = 3^3 \times 3$

Step 1: Simplify the right-hand side

The right-hand side of the equation involves exponents of 3. We can simplify it as follows:

$3^3 \times 3 = 3^4$

Thus, the equation becomes:

$x^7 = 3^4$

Step 2: Solve for $x$

To isolate $x$, we take the 7th root of both sides:

$x = (3^4)^{1/7}$

We can simplify this further using the property of exponents:

$x = 3^{4/7}$

Thus, the solution to the equation is:

$x = 3^{4/7}$

If you need a numerical value:

$x \approx 2.0801$

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:

1. How would the solution change if the exponent on $x$ were different, say $x^5$?
2. What happens if we had $3^4 \times 3^2$ on the right-hand side instead?
3. How can we use logarithms to solve this equation?
4. How does this problem change if we are solving for $x^7 = 3^5$?
5. What are the properties of exponents that allow us to simplify powers of numbers?

Tip: Always check if you can simplify both sides of an equation before solving for the variable—it often makes the problem much easier to manage!