https://file.aiquickdraw.com/mathbot/file/17248013813018vvr0g5z.jpg

The expression shown in the image is:

\[
\left(\frac{p^3 q^6}{a^4 b^{-2}}\right) \left(\frac{ab}{p^3 q}\right)
\]

### Step 1: Multiply the numerators and the denominators.

Let's multiply the expressions:

\[
\frac{p^3 q^6 \cdot ab}{a^4 b^{-2} \cdot p^3 q}
\]

### Step 2: Simplify the expression.

- For the \( p \) terms: \( p^3 \) in the numerator and \( p^3 \) in the denominator cancel out.
- For the \( q \) terms: \( q^6 \) in the numerator and \( q \) in the denominator simplify to \( q^{6-1} = q^5 \).
- For the \( a \) terms: \( a \) in the numerator and \( a^4 \) in the denominator simplify to \( a^{1-4} = a^{-3} \).
- For the \( b \) terms: \( b \) in the numerator and \( b^{-2} \) in the denominator simplify to \( b^{1+2} = b^3 \).

Now, the simplified expression is:

\[
\frac{q^5 b^3}{a^3}
\]

Thus, the simplified form of the expression is:

\[
\frac{q^5 b^3}{a^3}
\]

Would you like further details or have any questions?

Here are some related questions:
1. How would the expression change if \( p \) was raised to a different power?
2. What if the exponents for \( a \) and \( b \) were negative in the numerator instead?
3. How can this expression be used in solving real-world problems?
4. What happens if all variables \( p \), \( q \), \( a \), and \( b \) were equal to 1?
5. How would you differentiate this expression with respect to \( q \)?

**Tip:** When simplifying algebraic expressions with exponents, always combine like terms and carefully handle the signs of exponents.

Learn how to simplify the algebraic expression involving exponents and fractions step-by-step. This problem covers key algebraic concepts such as exponents and fraction simplification. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation