https://file.aiquickdraw.com/mathbot/file/17289532774496yl0m362.jpg

In the image you've provided, I see a set of algebraic steps involving powers and fractions, leading to the expression for \( 4p^2 = \left( \frac{6}{q^3} \right) \).

Let's break down the steps that are visible:

1. The expression begins with \( 4p \cdot \frac{1}{2} - \frac{3}{2} \cdot \frac{4}{p} - \left( \frac{-6}{q} \right)^{-1} \).
2. The simplifications proceed step by step:
   - Convert the terms into simpler powers of \( p \), \( q \), and constants.
   - Apply negative exponents, such as \( p^{-2} \) and \( q^3 \), and reciprocal rules for terms inside parentheses.
3. The result at the bottom of the steps is \( 4p^2 = \frac{6}{q^3} \), which is boxed to highlight the solution.

This appears to be an example of simplifying an algebraic expression by using exponent rules and inverse properties.

Do you have any specific questions about the steps shown here, or would you like me to expand on any part of the solution?

Here are 5 related questions to explore:

1. How do you simplify algebraic expressions involving negative exponents?
2. How do you handle division in algebra when fractions and variables are involved?
3. What are the rules for multiplying powers with the same base?
4. How do you handle the reciprocal of a fraction raised to a negative power?
5. How would you solve for \( p \) in the final equation \( 4p^2 = \frac{6}{q^3} \)?

**Tip**: When dealing with negative exponents, remember that \( a^{-n} = \frac{1}{a^n} \), which is key to simplifying many expressions.

Simplify the algebraic expression: 4p * (1/2) - (3/2) * (4/p) - (-6/q)^(-1)

Learn how to simplify an algebraic expression involving negative exponents and fractions, including the solution for 4p^2 = (6/q^3). The problem uses exponent rules and the reciprocal property. Ideal for students in Grades 8-10.

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