Let's simplify the given expression: \((x^9)^0 (x^7)^2\).

### Step 1: Simplify \((x^9)^0\)
Any term raised to the power of 0 is equal to 1 (as long as the base is not 0). Therefore:
\[
(x^9)^0 = 1
\]

### Step 2: Simplify \((x^7)^2\)
When raising a power to another power, multiply the exponents:
\[
(x^7)^2 = x^{7 \times 2} = x^{14}
\]

### Step 3: Multiply the simplified expressions
Now, multiply the simplified terms:
\[
1 \cdot x^{14} = x^{14}
\]

Thus, the simplified expression is:
\[
x^{14}
\]

Would you like any further details or clarification on this solution?

---

Here are 5 follow-up questions:
1. How do you handle negative exponents in a similar expression?
2. What would happen if the exponent in \((x^9)^0\) was not zero?
3. How do you simplify expressions involving multiple variables?
4. What is the general rule for multiplying exponents with the same base?
5. How would you approach a more complex expression with additional terms?

**Tip:** Remember, any non-zero base raised to the power of 0 is always 1.

Learn how to simplify the expression (x^9)^0 (x^7)^2 using key exponent rules. This guide breaks down the simplification process into easy steps, demonstrating how to apply the zero exponent rule and the power of a power rule. 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