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!