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Divide Terms Involving Index Laws

In this worksheet, students will divide terms using index laws to simplify expressions.

'Divide Terms Involving Index Laws' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Let us first recap the third index law:

am ÷ an = am-n

 

We can use this to simplify algebraic expressions in the same way as we do when working with numbers.

When dividing two (or more!) numbers or variables which have the same base (big number), we can use the third index law to simplify the expressions. Simply subtract the powers.

x12 ÷ x6 = x6

If you have two or more numbers, you should remember to divide them as well.

16b8 ÷ 8b5 = 2b3

Match the expressions to their simplified form.

Column A

Column B

a&sup7; ÷ x²
a&sup6;
a&sup5; ÷ x²
a&sup9; ÷ x³
a&sup7; ÷ a² ÷ a³
a&sup7;

Simplify

x12 ÷ y3

Choose the correct answer.

y&sup5;

y&sup9;

1&sup5;

1&sup9;

Simplify 27x6 ÷ 3x3.

9x²

24x²

9x³

24x³

Which one of these expressions CAN be simplified using the laws of indices?

a³ ÷ a²

a&sup6; ÷ b&sup6;

x&sup7; ÷ y&sup5;

x&sup5; ÷ x&sup7;

Use laws of indices to decide which of the statements are true and which are false.

Which of the expressions above will simplify to 4x2?

16x&sup4; ÷ 4x²

24x¹0; ÷ 6x&sup8;

24x&sup8; ÷ 6x²

3x¹0; ÷ 2x&sup7;

Match the expressions to their simplified versions.

Column A

Column B

15x&sup8; ÷ 3x&sup4;
6x&sup6;
24x&sup5; ÷ 6x&sup4;
10x&sup-2;
12x&sup9; × 2x³
4x
33x ÷ 3x³
5x&sup4;

Which of the expressions below will simplify to give 3x2y3?

3x² ÷ 12x&sup4;

9x&sup4;y ÷ 2x&sup4;y&sup5;

45x&sup6;y&sup7; ÷ 15x&sup4;y&sup4;

6x&sup8; ÷ 6y&sup6;

Simplify  10a7b6c5 ÷ 2abc.

8a&sup6;b&sup5;c&sup4;

5a&sup6;b&sup5;c&sup4;

5a&sup7;b&sup6;c&sup5;

8a&sup7;b&sup6;c&sup5;

Simplify 20w3x5 ÷ 5wx3 &divide 2wx.

13w³x

13wx

2w³x

2wx

  • Question 1

Match the expressions to their simplified form.

CORRECT ANSWER

Column A

Column B

a&sup7; ÷ x²
a&sup7;
a&sup5; ÷ x²
a&sup9; ÷ x³
a&sup6;
a&sup7; ÷ a² ÷...
EDDIE SAYS
Remember, when you divide with powers of the same number, you can just SUBTRACT the powers.
  • Question 2

Simplify

x12 ÷ y3

Choose the correct answer.

CORRECT ANSWER
y&sup9;
EDDIE SAYS
Both terms have y as a base, so we can just subtract the powers to get the answer. 12 − 3 = 9 Remember to keep the base number! The correct answer is y&sup9;.
  • Question 3

Simplify 27x6 ÷ 3x3.

CORRECT ANSWER
9x³
EDDIE SAYS
Remember to divide first: 27 ÷ 3 = 9, then apply the laws of indices to x&sup6; ÷ x³ = x³. The final answer is 9x³
  • Question 4

Which one of these expressions CAN be simplified using the laws of indices?

CORRECT ANSWER
a³ ÷ a²
x&sup5; ÷ x&sup7;
EDDIE SAYS
Laws of indices can only be used if we have the same base number/variable. Middle two options have the same powers, but the letters are different, so we cannot simplify them using the laws of indices.
  • Question 5

Use laws of indices to decide which of the statements are true and which are false.

CORRECT ANSWER
EDDIE SAYS
Did you spot the false statements? x&sup5; ÷ x&sup7; = x² -> 5 - 7 = -2, so there should be a NEGATIVE 2 as the power. p&sup6; ÷ p³ = p² -> the indices should have been subtracted giving p³.
  • Question 6

Which of the expressions above will simplify to 4x2?

CORRECT ANSWER
16x&sup4; ÷ 4x²
24x¹0; ÷ 6x&sup8;
EDDIE SAYS
Only the first two expressions can be simplified to give 4x².
  • Question 7

Match the expressions to their simplified versions.

CORRECT ANSWER

Column A

Column B

15x&sup8; ÷ 3x&sup4;
5x&sup4;
24x&sup5; ÷ 6x&sup4;
4x
12x&sup9; × 2x³
6x&sup6;
33x ÷ 3x³
10x&sup-2;
EDDIE SAYS
To find the matching answers, divide the big numbers first and use index laws to work out what power x needs to take: simply subtract the powers. Remember, if there is no power next to the letter, the value of the power is 1.
  • Question 8

Which of the expressions below will simplify to give 3x2y3?

CORRECT ANSWER
9x&sup4;y ÷ 2x&sup4;y&sup5;
45x&sup6;y&sup7; ÷ 15x&sup4;y&sup4;
EDDIE SAYS
The numbers need to divide to give 3, so the first option is definitely wrong. Only two of the remaining options are correct. Have you checked the indices? When you subtract powers of x, they should make 2. The powers of y should make 3 when you subtract them.
  • Question 9

Simplify  10a7b6c5 ÷ 2abc.

CORRECT ANSWER
5a&sup6;b&sup5;c&sup4;
EDDIE SAYS
Let's break this equestion down: 10 ÷ 2 = 5 a&sup7; ÷ a = a&sup6; b&sup6; ÷ b = b&sup5; c&sup5; ÷ c = c&sup4; The final answer is 5a&sup6;b&sup5;c&sup4;.
  • Question 10

Simplify 20w3x5 ÷ 5wx3 &divide 2wx.

CORRECT ANSWER
2wx
EDDIE SAYS
There're three parts to divide here, but you still need to follow the same rules. 20 ÷ 5 ÷ 2 = 2 w³ ÷ w ÷ w = w x&sup5; ÷ x³ ÷ x = x The final answer is 2wx.
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