https://file.aiquickdraw.com/mathbot/file/17267051321881qsuq0db.jpg

The expression in the image is:

\[
\frac{x^{14} \cdot x^5}{x^7}
\]

Let's simplify this step by step.

### Step 1: Apply the product of powers rule
When multiplying two terms with the same base, you add their exponents:

\[
x^{14} \cdot x^5 = x^{14 + 5} = x^{19}
\]

### Step 2: Apply the quotient of powers rule
When dividing terms with the same base, subtract the exponent of the denominator from the exponent of the numerator:

\[
\frac{x^{19}}{x^7} = x^{19 - 7} = x^{12}
\]

### Final Simplified Expression:
\[
x^{12}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you simplify \(\frac{x^8 \cdot x^3}{x^4}\)?
2. What is the result of \(\frac{y^{15} \cdot y^5}{y^6}\)?
3. How can you simplify \(\frac{a^{10} \cdot a^2}{a^8}\)?
4. What happens when the exponents in the numerator and denominator are equal?
5. How would you handle an expression like \(\frac{x^5 \cdot x^{-2}}{x^3}\)?

**Tip:** Remember that multiplying terms with the same base involves adding exponents, while dividing terms involves subtracting exponents!

Learn how to simplify the algebraic expression x^14 * x^5 / x^7 using exponent rules. This step-by-step solution explains the product of powers and quotient of powers concepts. Suitable for students in Grades 7-9.

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