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?

---

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!

Learn how to solve the exponential equation x^7 = 3^3 × 3 with step-by-step simplification using the laws of exponents. The solution explores key algebraic techniques to find the value of x. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation