1. **Express 12/5 as a mixed fraction in the form a (b/c)** Step 1: Divide 12 by 5 to find the whole number part. $$12 \div 5 = 2 \text{ remainder } 2$$ Step 2: Write the remainder as the numerator and the divisor as the denominator. So, $$12/5 = 2 \frac{2}{5}$$ --- 2. **Evaluate $3^4$** Step 1: Recall that $a^n$ means multiply $a$ by itself $n$ times. $$3^4 = 3 \times 3 \times 3 \times 3 = 81$$ --- 3. **Evaluate $5^0$** Step 1: Any nonzero number raised to the power 0 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, exponent applies before the negative sign. $$-4^2 = -(4^2) = -16$$ --- 6. **Simplify $a^4 \times a^3$** Step 1: When multiplying powers with the same base, add exponents. $$a^4 \times a^3 = a^{4+3} = a^7$$ --- 7. **Simplify $\frac{t^9}{t^5}$** Step 1: When dividing powers with the same base, subtract exponents. $$\frac{t^9}{t^5} = t^{9-5} = t^4$$ --- 8. **Simplify $p(p^2)^3$** Step 1: Apply power to a power rule: $(a^m)^n = a^{mn}$. $$(p^2)^3 = p^{2 \times 3} = p^6$$ Step 2: Multiply powers with the same base by adding exponents. $$p \times p^6 = p^{1+6} = p^7$$ --- 9. **Simplify $(3x^2)^3$** Step 1: Apply power to each factor inside parentheses. $$(3)^3 = 27$$ $$(x^2)^3 = x^{2 \times 3} = x^6$$ Step 2: Multiply results. $$(3x^2)^3 = 27x^6$$ --- 10. **Evaluate $3 - \frac{2}{3}$** Step 1: Convert 3 to a fraction with denominator 3. $$3 = \frac{9}{3}$$ Step 2: Subtract fractions. $$\frac{9}{3} - \frac{2}{3} = \frac{9-2}{3} = \frac{7}{3}$$ Step 3: Express as mixed fraction. $$\frac{7}{3} = 2 \frac{1}{3}$$ --- 11. **Evaluate $-\frac{2}{3} \div \frac{1}{7}$** Step 1: Dividing by a fraction is multiplying by its reciprocal. $$-\frac{2}{3} \div \frac{1}{7} = -\frac{2}{3} \times \frac{7}{1}$$ Step 2: Multiply numerators and denominators. $$= -\frac{2 \times 7}{3 \times 1} = -\frac{14}{3}$$ Step 3: Express as mixed fraction. $$-\frac{14}{3} = -4 \frac{2}{3}$$