1. Write as a single power **a.** $3^2 \times 3 = 3^{2+1} = 3^3$ **b.** $7 \times 7^3 = 7^{1+3} = 7^4$ **c.** $12 \times 12^5 = 12^{1+5} = 12^6$ **d.** $15^4 \times 15 = 15^{4+1} = 15^5$ 2. Write as a single power **a.** $6^3 \times 6^3 = 6^{3+3} = 6^6$ **b.** $10^5 \times 10^2 = 10^{5+2} = 10^7$ **c.** $3^6 \times 3^3 = 3^{6+3} = 3^9$ **d.** $14^3 \times 14^4 = 14^{3+4} = 14^7$ 4. Write as a single power **a.** $(5^3)^2 = 5^{3 \times 2} = 5^6$ **b.** $(15^3)^2 = 15^{3 \times 2} = 15^6$ **c.** $(7^3)^3 = 7^{3 \times 3} = 7^9$ **d.** $(3^4)^5 = 3^{4 \times 5} = 3^{20}$ 5. Write as a power **a.** $4 = 2^2$ **b.** $4^3 = (2^2)^3 = 2^{2 \times 3} = 2^6$ **c.** $9^3 = (3^2)^3 = 3^{2 \times 3} = 3^6$ 6. Write as a power of 5 Given $5^4 = 625$ **a.** $625^2 = (5^4)^2 = 5^{4 \times 2} = 5^8$ **b.** $625^3 = (5^4)^3 = 5^{4 \times 3} = 5^{12}$ **c.** $625^4 = (5^4)^4 = 5^{4 \times 4} = 5^{16}$ 7. Find the missing power **a.** $4^2 \times 4^\square = 4^5 \Rightarrow 2 + \square = 5 \Rightarrow \square = 3$ **b.** $7^4 \times 7^\square = 7^6 \Rightarrow 4 + \square = 6 \Rightarrow \square = 2$ **c.** $15^3 \times 15^\square = 15^6 \Rightarrow 3 + \square = 6 \Rightarrow \square = 3$ **d.** $15^\square \times 15^4 = 15^4 \Rightarrow \square + 4 = 4 \Rightarrow \square = 0$ 8. Work out and write the answer in index form **a.** $8^3 \div 8 = 8^{3-1} = 8^2$ **b.** $5^6 \div 5^2 = 5^{6-2} = 5^4$ **c.** $2^{10} \div 2^2 = 2^{10-2} = 2^8$ **d.** $3^6 \div 3^3 = 3^{6-3} = 3^3$ **e.** $12^4 \div 12^4 = 12^{4-4} = 12^0 = 1$ 9. Find the missing power of 6 **a.** $6^5 \div 6^\square = 6^2 \Rightarrow 5 - \square = 2 \Rightarrow \square = 3$ **b.** $6^8 \div 6^\square = 6^4 \Rightarrow 8 - \square = 4 \Rightarrow \square = 4$ **c.** $6^\square \div 6^2 = 6^6 \Rightarrow \square - 2 = 6 \Rightarrow \square = 8$ **d.** $6^\square \div 6^3 = 6^3 \Rightarrow \square - 3 = 3 \Rightarrow \square = 6$ 10. Work out and write the answer in index form **a.** $4^5 \div 2^3 = (2^2)^5 \div 2^3 = 2^{10} \div 2^3 = 2^{10-3} = 2^7$ **b.** $9^4 \div 3^5 = (3^2)^4 \div 3^5 = 3^8 \div 3^5 = 3^{8-5} = 3^3$ **c.** $32^2 \div 2^6 = (2^5)^2 \div 2^6 = 2^{10} \div 2^6 = 2^{10-6} = 2^4$ **d.** $27^2 \div 3^6 = (3^3)^2 \div 3^6 = 3^6 \div 3^6 = 3^{6-6} = 3^0 = 1$ 11. Write as a power of 5 **a.** $125 = 5^3$ **b.** $125^2 = (5^3)^2 = 5^{3 \times 2} = 5^6$ **c.** $125^4 = (5^3)^4 = 5^{3 \times 4} = 5^{12}$