https://file.aiquickdraw.com/mathbot/file/17296889041303oiodjr3.jpg

The expression shown in the image is:

\[
\left( 2x^3 y^{-3} \right)^{-2}
\]

To simplify this, we will apply the power of a power rule, which states \((a^m)^n = a^{m \cdot n}\), and the rule that \((ab)^n = a^n \cdot b^n\).

1. Apply the exponent of \(-2\) to each part inside the parentheses:
   \[
   = 2^{-2} \cdot (x^3)^{-2} \cdot (y^{-3})^{-2}
   \]

2. Simplify the powers:
   \[
   = \frac{1}{2^2} \cdot x^{-6} \cdot y^{6}
   \]

3. Final expression:
   \[
   = \frac{y^6}{4x^6}
   \]

Would you like more details or further explanation?

Here are some related questions:
1. What are the power rules in exponents?
2. How do negative exponents work in simplifications?
3. Can you explain why \((x^a)^b = x^{ab}\)?
4. What happens when a negative exponent is applied to a fraction?
5. How do we simplify expressions with variables raised to powers?

**Tip**: When simplifying complex expressions, always apply the exponent rules step by step to avoid errors.

Simplify the exponent expression (2x^3 y^{-3})^{-2} step by step using the power of a power rule and negative exponent rules. This algebra problem covers key concepts related to exponents and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation