1. Express $\frac{12}{5}$ as a mixed fraction in the form $a \frac{b}{c}$. Step 1: Divide 12 by 5. $$12 \div 5 = 2 \text{ remainder } 2$$ Step 2: Write the mixed fraction using the quotient and remainder. $$2 \frac{2}{5}$$ So, $\frac{12}{5} = 2 \frac{2}{5}$. 2. Evaluate $3^4$. Step 1: Use the definition of exponents: $a^n = a \times a \times \cdots \times a$ ($n$ times). $$3^4 = 3 \times 3 \times 3 \times 3 = 81$$ 3. Evaluate $5^0$. Step 1: Any nonzero number raised to the zero power is 1. $$5^0 = 1$$ 4. Evaluate $(-3)^2$. Step 1: Square the number inside the parentheses. $$(-3)^2 = (-3) \times (-3) = 9$$ 5. Evaluate $-4^2$. Step 1: According to order of operations, exponentiation comes before the negative sign. $$-4^2 = -(4^2) = -16$$ 6. Simplify $a^4 \times a^3$. Step 1: Use the rule $a^m \times a^n = a^{m+n}$. $$a^4 \times a^3 = a^{4+3} = a^7$$ 7. Simplify $\frac{t^9}{t^5}$. Step 1: Use the rule $\frac{a^m}{a^n} = a^{m-n}$. $$\frac{t^9}{t^5} = t^{9-5} = t^4$$ 8. Simplify $p (p^2)^3$. Step 1: Use the rule $(a^m)^n = a^{m \times n}$. $$(p^2)^3 = p^{2 \times 3} = p^6$$ Step 2: Multiply $p$ by $p^6$ using $a^m \times a^n = a^{m+n}$. $$p \times p^6 = p^{1+6} = p^7$$ 9. Simplify $(3x^2)^3$. Step 1: Apply the exponent to each factor inside the parentheses. $$(3)^3 = 27$$ $$(x^2)^3 = x^{2 \times 3} = x^6$$ Step 2: Multiply the results. $$27 x^6$$ 10. Evaluate $3 - \frac{2}{3}$. Step 1: Convert 3 to a fraction with denominator 3. $$3 = \frac{9}{3}$$ Step 2: Subtract the fractions. $$\frac{9}{3} - \frac{2}{3} = \frac{9-2}{3} = \frac{7}{3}$$ 11. Evaluate $-\frac{2}{3} \div \frac{1}{7}$. Step 1: Division of fractions is multiplication by the reciprocal. $$-\frac{2}{3} \div \frac{1}{7} = -\frac{2}{3} \times \frac{7}{1}$$ Step 2: Multiply numerators and denominators. $$-\frac{2 \times 7}{3 \times 1} = -\frac{14}{3}$$ Final answers: 1. $2 \frac{2}{5}$ 2. $81$ 3. $1$ 4. $9$ 5. $-16$ 6. $a^7$ 7. $t^4$ 8. $p^7$ 9. $27 x^6$ 10. $\frac{7}{3}$ 11. $-\frac{14}{3}$