https://file.aiquickdraw.com/mathbot/file/17302735430718kybnvx8.jpg

To solve the equation:

\[
\left(10^{6x}\right)\left(10^{8x}\right) = 10^{10}
\]

### Step-by-Step Solution

1. **Combine the Powers of 10 on the Left Side**:
   Since the two terms on the left are multiplied, we can add their exponents:
   \[
   10^{6x} \times 10^{8x} = 10^{(6x + 8x)} = 10^{14x}
   \]

2. **Rewrite the Equation**:
   Now the equation becomes:
   \[
   10^{14x} = 10^{10}
   \]

3. **Set the Exponents Equal to Each Other**:
   Since the bases (10) are the same, we can set the exponents equal:
   \[
   14x = 10
   \]

4. **Solve for \( x \)**:
   Divide both sides by 14:
   \[
   x = \frac{10}{14} = \frac{5}{7}
   \]

### Final Answer
\[
x = \frac{5}{7}
\]

Would you like more details on any part of this solution, or have any questions?

### Related Questions:
1. How would the solution change if the base was not 10 but another number?
2. How does this problem change if we multiply different powers, like \(10^{6x}\) and \(10^{7x}\)?
3. What if the equation was \(10^{14x} = 10^{12}\) instead?
4. Can we solve similar problems with different bases, like \(2^{6x}\) and \(2^{8x}\)?
5. What steps would you take if the equation had additional terms on one side?

#### Tip:
When dealing with exponents, remember that multiplying terms with the same base means adding exponents, and dividing terms with the same base means subtracting exponents.

The solution of (10^6x)(10^8x) = 10^10 is x = ____.

Learn how to solve the exponential equation (10^6x)(10^8x) = 10^10 step-by-step. This solution covers the rules of exponents, combining powers, and setting exponents equal for matching bases. Suitable for high school students in Grades 9-10.

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