We are given the equation:

\[
216^{2x - 3} = 6^{x - 4}
\]

### Step 1: Express 216 and 6 as powers of the same base
We know that \( 216 = 6^3 \), so we can rewrite \( 216^{2x - 3} \) as:

\[
216^{2x - 3} = (6^3)^{2x - 3}
\]

Using the power of a power rule \( (a^m)^n = a^{mn} \), we get:

\[
(6^3)^{2x - 3} = 6^{3(2x - 3)} = 6^{6x - 9}
\]

Now, the original equation becomes:

\[
6^{6x - 9} = 6^{x - 4}
\]

### Step 2: Equate the exponents
Since the bases are the same (both are base 6), we can equate the exponents:

\[
6x - 9 = x - 4
\]

### Step 3: Solve for \( x \)
Now, solve the equation:

\[
6x - x = -4 + 9
\]

\[
5x = 5
\]

\[
x = 1
\]

### Final Answer:
The solution is \( x = 1 \).

Would you like any more details or have any other questions?

Here are 5 related questions:
1. How do you simplify equations with exponents?
2. What is the power of a power rule in exponents?
3. How can you solve an equation where the bases are the same?
4. What happens if the bases in an equation are not the same?
5. How do you factor exponential expressions?

**Tip:** Always try to express different numbers as powers of the same base when solving exponential equations.

If 216^2x − 3 = 6^x − 4, then find the value of x.

Discover how to solve the exponential equation 216^2x - 3 = 6^x - 4 by using the power of a power rule and equating exponents. Follow a detailed, step-by-step explanation suitable for students in Grades 10-12. Learn key concepts in exponential equations and algebra.

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If 216^2x − 3

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