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Let's simplify the given expression:

\[
\frac{23x^{18}y^{15}}{22x^7y^6}
\]

We will simplify both the numerical coefficients and the variables separately.

### Step 1: Simplify the coefficients
The coefficients are \( 23 \) and \( 22 \). Since these numbers don't have any common factors, we cannot simplify them further, so the coefficient remains as:
\[
\frac{23}{22}
\]

### Step 2: Simplify the \( x \)-terms
The powers of \( x \) in the expression are \( x^{18} \) in the numerator and \( x^7 \) in the denominator. We subtract the exponents:
\[
x^{18 - 7} = x^{11}
\]

### Step 3: Simplify the \( y \)-terms
The powers of \( y \) in the expression are \( y^{15} \) in the numerator and \( y^6 \) in the denominator. We subtract the exponents:
\[
y^{15 - 6} = y^9
\]

### Final Answer
Combining all the simplified parts, we get:
\[
\frac{23x^{11}y^9}{22}
\]

Would you like more details or have any questions about this simplification?

Here are five related questions to expand your understanding:
1. What happens if both the numerator and denominator have coefficients with a common factor?
2. How do you simplify expressions with negative exponents?
3. What is the rule for dividing terms with the same base?
4. How would you handle a situation where there are variables in the coefficients?
5. How can you check your simplification for accuracy?

**Tip:** When dividing powers with the same base, always subtract the exponent in the denominator from the exponent in the numerator.

Simplify the expression completely: (23x^18 y^15) / (22x^7 y^6)

Learn how to simplify the expression (23x^18 y^15) / (22x^7 y^6) step-by-step. This problem covers key algebraic concepts like exponents and simplifying expressions. Suitable for students in Grades 8-10.

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