https://file.aiquickdraw.com/mathbot/file/17297854583491nolm1by.jpg

Let's simplify the expressions one by one.

### a. \((4x^3)^2\)
Using the rule \((a^m)^n = a^{m \cdot n}\), we can simplify:
\[
(4x^3)^2 = 4^2 \cdot (x^3)^2 = 16x^6
\]

### b. \(\left(\frac{-2}{x}\right)^3\)
Here, apply the power rule to both the numerator and the denominator:
\[
\left(\frac{-2}{x}\right)^3 = \frac{(-2)^3}{x^3} = \frac{-8}{x^3}
\]

### c. \((5x^2y^4)^2\)
Using the same power rule, apply the exponent to each term:
\[
(5x^2y^4)^2 = 5^2 \cdot (x^2)^2 \cdot (y^4)^2 = 25x^4y^8
\]

### Final Answers:
a. \( 16x^6 \)  
b. \( \frac{-8}{x^3} \)  
c. \( 25x^4y^8 \)

Would you like more details or explanations on any of these steps? 

Here are 5 related questions for further practice:
1. Simplify \((3x^2y)^3\).
2. Simplify \(\left(\frac{-3x^2}{2}\right)^2\).
3. What is the result of \((2x^5y^2)^3\)?
4. Expand \(\left(\frac{4x^3}{y}\right)^2\).
5. Simplify \((7x^2y^3)^4\).

**Tip:** When simplifying expressions with powers, make sure to apply the exponent to every term inside the parentheses.

Simplify each of the following: a. (4x^3)^2, b. (-2/x)^3, c. (5x^2y^4)^2

Learn how to simplify exponential expressions like (4x^3)^2, (-2/x)^3, and (5x^2y^4)^2 using the laws of exponents. This guide walks through key concepts and formulas, making it ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation