https://file.aiquickdraw.com/mathbot/file/1726013703926mvpugbea.jpg

The expression shown in the image is:

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

To simplify this expression, we apply the power of a fraction rule, which states:

\[
\left( \frac{A}{B} \right)^n = \frac{A^n}{B^n}
\]

Here, \( A = -2a^4 \) and \( B = 3b^2 \), and the exponent is 3. So we raise both the numerator and denominator to the power of 3.

### Step-by-step simplification:

1. Apply the exponent to the numerator and denominator:
\[
\left( \frac{-2a^4}{3b^2} \right)^3 = \frac{(-2a^4)^3}{(3b^2)^3}
\]

2. Simplify the numerator:
\[
(-2a^4)^3 = (-2)^3 \cdot (a^4)^3 = -8a^{12}
\]

3. Simplify the denominator:
\[
(3b^2)^3 = 3^3 \cdot (b^2)^3 = 27b^6
\]

Thus, the simplified expression is:

\[
\frac{-8a^{12}}{27b^6}
\]

Would you like more details on how the rules were applied?

Here are 5 related questions for further practice:
1. What is the result of \(\left( \frac{5x^2}{4y} \right)^2\)?
2. How do you simplify \(\left( \frac{-3m^5}{2n^3} \right)^4\)?
3. What is \(\left( \frac{-7p^3}{5q^2} \right)^2\)?
4. Can you explain how to distribute exponents when both the base and exponent are negative?
5. How do you handle negative exponents in expressions like \(\left( \frac{-x^2}{y} \right)^{-3}\)?

**Tip**: Always be careful with negative bases raised to an odd power—they will remain negative.

Simplify the expression: (-2a^4 / 3b^2)^3

Learn how to simplify the algebraic expression (-2a^4 / 3b^2)^3 by applying exponent rules and simplifying the result. Suitable for students in Grades 8-10, covering key concepts in algebra and exponents.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation