https://file.aiquickdraw.com/mathbot/file/1727894717759996gub1u.jpg

The expression given in the image is:

\[
\left( 12x^4 y^6 z^8 \right)^2
\]

To simplify this, we'll apply the power rule for exponents: \((a^m)^n = a^{m \cdot n}\). This rule states that when raising a power to another power, you multiply the exponents.

### Step-by-step solution:
1. Simplify the constant \(12^2\):
   \[
   12^2 = 144
   \]

2. Apply the exponent rule to each variable:
   - \(x^4\) becomes \((x^4)^2 = x^{4 \cdot 2} = x^8\)
   - \(y^6\) becomes \((y^6)^2 = y^{6 \cdot 2} = y^{12}\)
   - \(z^8\) becomes \((z^8)^2 = z^{8 \cdot 2} = z^{16}\)

### Final simplified expression:
\[
144x^8 y^{12} z^{16}
\]

Would you like more details or have any further questions on this?

Here are 5 related questions for practice:
1. How would you simplify \(\left(5a^3 b^2\right)^4\)?
2. What is the simplified form of \(\left(2x^2 y^3\right)^3\)?
3. How do you simplify \(\left(7p^5 q^2 r^3\right)^2\)?
4. What happens when you raise a product of terms to a power?
5. How can you simplify \(\left(3m^4 n^6\right)^3\)?

**Tip:** Always apply the power rule for exponents carefully when distributing a power across multiple terms!

Simplify (12x^4 y^6 z^8)^2 and express your answer using exponents.

Learn how to simplify the expression (12x^4 y^6 z^8)^2 using the power rule for exponents. This step-by-step solution covers exponentiation and algebraic simplifications, 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