Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
GCSE Maths Starter 5
1)
5. Copy the shape below
into your exercise books
and draw 5 more
shapes that tessellate
with it..
2. Increase £240 by 35%.
3. What is 159 x 72
4. Solve: 3(x+1) = 24
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
• To find the value of calculations using indices.
• To simplify letters and numbers when they are
being X, +, -, ÷.
• To use index laws to simplify and calculate the
value of numerical expressions involving
multiplication and division of integer powers,
and of powers of a power
EXTN: To simplify expressions with more than
one letter and numbers. (Grade C)
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
• How can I simplify: 45 x 43?
4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 48
• How can I simplify: 79 x 76?
7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 715
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
26 x 2 4
24 x 2 2
= 210
= 26
35 x 3 7
= 312
General Rule:
When multiplying terms with the same base, you
add the powers
EXAMPLE: 47 x 45 = 47+5 = 412
am x an = am+n
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
• How can I simplify 95 ÷ 93?
9x9x9x9x9
= 9 x 9 = 92
9x9x9
• How can I simplify 117 ÷ 112?
11 x 11 x 11 x 11 x 11 x 11 x 11
11 x 11
= 115
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
26 ÷ 2 4
25 ÷ 2 2
35 ÷ 3 7
= 22
= 23
= 3-2
General Rule
When dividing terms with the same base, you
subtract the powers
EXAMPLE: 47 ÷ 45 = 47-5 = 42
am ÷ an = am-n
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
• How can I simplify
4
3
(4 ) ?
4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 412
• How can I simplify
5
2
(7 ) ?
7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 710
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
(26)2
= 26 x 26 = 212
(35)3
= 35 x 3 5 x 3 5
= 315
General Rule:
When raising a power to another power, you
multiply the powers
(am)n = am x n
EXAMPLE:
5
7
(4 ) =
47 x 5 = 435
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
• Simplify the following:
73 x 78
75
𝑥4 x 𝑥9
𝑥5 x 𝑥10
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
• How can I simplify 5a3 x 6a7?
5xaxaxa x 6xaxaxaxaxaxaxa
5 x 6 x a x a x a x a x a x a x a x a x a x a = 30a10
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 102/111.
Lesson 5 Index Laws and
Simplifying Algebra.
Mathswatch 111.
• To find the value of calculations using indices.
• To simplify letters and numbers when they are
being X, +, -, ÷.
• To use index laws to simplify and calculate the
value of numerical expressions involving
multiplication and division of integer powers,
and of powers of a power
EXTN: To simplify expressions with more than
one letter and numbers. (Grade C)