Use the product rule to simplify the expression. Write the results using exponents. $$ (-2)^{4} \cdot(-2)^{9} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ (-2)^{4} \cdot (-2)^{9} $$ using the **product rule of exponents**, follow these steps:

### **Product Rule of Exponents**
The product rule states that when you multiply two expressions with the same base, you can add their exponents:

$$
a^{m} \cdot a^{n} = a^{m+n}
$$

### **Applying the Rule**
Given the expression:

$$
(-2)^{4} \cdot (-2)^{9}
$$

1. **Identify the Base and Exponents:**
   - Base ($$a$$): $$-2$$
   - Exponents ($$m$$ and $$n$$): 4 and 9

2. **Apply the Product Rule:**

$$
(-2)^{4} \cdot (-2)^{9} = (-2)^{4+9} = (-2)^{13}
$$

### **Final Simplified Expression**

$$
(-2)^{13}
$$

This is the simplified form using exponents.
$$ (-2)^{13} $$

Use the product rule to simplify the expression. Write the results using exponents. \( (-2)^{4} \cdot(-2)^{9} \)