https://file.aiquickdraw.com/mathbot/file/1727916519625katkv0jf.jpg

Let's go through the questions from the image step by step.

### Question 2: Simplify expressions using one exponent
1. **a. \( 140x^5 \cdot x \)**
   - Combine like terms. Recall that when multiplying terms with the same base, you add the exponents.
   \[
   140x^5 \cdot x = 140x^{5+1} = 140x^6
   \]

2. **b. \( (1.04)^3 \cdot 1.04 \)**
   - Again, apply the rule of exponents: \( a^m \cdot a^n = a^{m+n} \).
   \[
   (1.04)^3 \cdot 1.04 = (1.04)^{3+1} = (1.04)^4
   \]

3. **c. \( (x^5)^4 \)**
   - Use the power rule for exponents: \( (a^m)^n = a^{m \cdot n} \).
   \[
   (x^5)^4 = x^{5 \cdot 4} = x^{20}
   \]

---

### Question 3: Simplify expressions using one exponent
1. **a. \( (x^4)^3 \)**
   - Apply the power rule.
   \[
   (x^4)^3 = x^{4 \cdot 3} = x^{12}
   \]

2. **b. \( x^3 \cdot x^6 \)**
   - Use the multiplication rule for exponents.
   \[
   x^3 \cdot x^6 = x^{3+6} = x^9
   \]

3. **c. \( \frac{x^7}{x^6} \)**
   - Use the division rule for exponents: \( \frac{a^m}{a^n} = a^{m-n} \).
   \[
   \frac{x^7}{x^6} = x^{7-6} = x^1 = x
   \]

4. **d. \( x^4 \cdot (x^3)^3 \)**
   - First simplify \( (x^3)^3 \) using the power rule.
   \[
   (x^3)^3 = x^{3 \cdot 3} = x^9
   \]
   Now multiply the terms:
   \[
   x^4 \cdot x^9 = x^{4+9} = x^{13}
   \]

Would you like to go over any specific details or questions?

### 5 Additional Related Questions:
1. How do you simplify \( (2x^5 \cdot y^3)^2 \)?
2. What is the simplified form of \( \frac{y^8}{y^2 \cdot y^3} \)?
3. How do you combine \( 3a^2 \cdot 5a^7 \)?
4. What is the result of \( \frac{b^{12}}{b^4} \cdot b^6 \)?
5. How do you simplify \( (4m^2n^3)^3 \)?

### Tip:
Always remember the exponent rules: product, quotient, and power rules. They help simplify expressions more easily!

Simplify these expressions using one exponent: 140x^5 * x, (1.04)^3 * 1.04, (x^5)^4, (x^4)^3, x^3 * x^6, x^7 / x^6, x^4 * (x^3)^3

Simplify algebraic expressions involving exponents using product, power, and quotient rules. This exercise is suitable for students in Grades 7-9 and covers key concepts like combining exponents with the same base and simplifying expressions like (x^4)^3 and 140x^5 * x.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation