1) Simplify the expression $m^{-6} \div m^{7} \times m^{2}$. 2) Simplify the expression $m^{-6} \times m^{7} \div m^{2}$. --- ### Step 1: Recall the laws of exponents - When dividing powers with the same base: $a^{m} \div a^{n} = a^{m-n}$. - When multiplying powers with the same base: $a^{m} \times a^{n} = a^{m+n}$. --- ### Problem 1: Simplify $m^{-6} \div m^{7} \times m^{2}$ 1. Apply division first: $$m^{-6} \div m^{7} = m^{-6-7} = m^{-13}$$ 2. Now multiply by $m^{2}$: $$m^{-13} \times m^{2} = m^{-13+2} = m^{-11}$$ **Final answer for 1:** $m^{-11}$ --- ### Problem 2: Simplify $m^{-6} \times m^{7} \div m^{2}$ 1. Multiply first: $$m^{-6} \times m^{7} = m^{-6+7} = m^{1}$$ 2. Now divide by $m^{2}$: $$m^{1} \div m^{2} = m^{1-2} = m^{-1}$$ **Final answer for 2:** $m^{-1}$