Laws of indices questions with answers

Questions

1. Question 1Multiplying: add the indices

   Simplify $4a^{5} \times 2a^{4}$.

   Show the worked solution

   1. Step 1: Simplify the numbers, then the power of each letterNumbers: $4 \times 2 = 8$$a$: add the indices, $5 + 4 = 9$
   2. Step 2: Answer$8a^{9}$
2. Question 2Multiplying: add the indices

   Simplify $a^{3} \times 2a^{6}$.

   Show the worked solution

   1. Step 1: Simplify the numbers, then the power of each letterNumbers: $1 \times 2 = 2$$a$: add the indices, $3 + 6 = 9$
   2. Step 2: Answer$2a^{9}$
3. Question 3Dividing: subtract the indices

   Simplify $\dfrac{3a^{8}}{a}$.

   Show the worked solution

   1. Step 1: Simplify the numbers, then the power of each letterNumbers: $\dfrac{3}{1} = 3$$a$: subtract the indices, $8 - 1 = 7$
   2. Step 2: Answer$3a^{7}$
4. Question 4Dividing: subtract the indices

   Simplify $\dfrac{6a^{7}}{2a^{4}}$.

   Show the worked solution

   1. Step 1: Simplify the numbers, then the power of each letterNumbers: $\dfrac{6}{2} = 3$$a$: subtract the indices, $7 - 4 = 3$
   2. Step 2: Answer$3a^{3}$
5. Question 5Power of a power: multiply the indices

   Simplify $(5a^{3})^{2}$.

   Show the worked solution

   1. Step 1: Simplify the number in front, then the power of each letterNumbers: $5^{2} = 25$$a$: multiply the indices, $3 \times 2 = 6$
   2. Step 2: Answer$25a^{6}$
6. Question 6Power of a power: multiply the indices

   Simplify $(2a^{5})^{2}$.

   Show the worked solution

   1. Step 1: Simplify the number in front, then the power of each letterNumbers: $2^{2} = 4$$a$: multiply the indices, $5 \times 2 = 10$
   2. Step 2: Answer$4a^{10}$