ALGEBRA 7 INDICES
MULTIPLYING INDICES
When multiplying indices with the same base ADD their powers
Example: x² x x⁴ = x⁸ since 2 x 4 = 8
This is the same as : xx x xxxx = xxxxxxxx
Example with numbers and variables combined: 3x² x 5x³ = 15x⁵ since 3 x 5 = 15 and x² x x³ = x⁵
This can be expressed as a rule:
Example: x² x x⁴ = x⁸ since 2 x 4 = 8
This is the same as : xx x xxxx = xxxxxxxx
Example with numbers and variables combined: 3x² x 5x³ = 15x⁵ since 3 x 5 = 15 and x² x x³ = x⁵
This can be expressed as a rule:
ACTIVITY 1
Simplify these expressions:
1) x² x x⁷ =
2) p⁴ x p⁴ =
3) w⁴ x w x w⁵ =
4) 3y⁴ x 6y⁵ =
5) 2x⁴ x 7y³ =
6) 6r⁴ x 2r x 4r² =
7) -5a⁴ x 4a² =
8)1/2a³ x 1/2a² =
9) 2x²y⁴ x 3x³y² x xy =
10) 0.3m⁴ x 0.3m x -0.3m² =
answers: 1) x⁹ 2) p⁸ 3) w¹º 4) 18y⁹ 5) 14x⁴y³ 6) 48r⁷ 7) -20a⁶ 8) 1/4a⁵ 9) 6x⁶y⁷ 10) -0.027m⁷
Simplify these expressions:
1) x² x x⁷ =
2) p⁴ x p⁴ =
3) w⁴ x w x w⁵ =
4) 3y⁴ x 6y⁵ =
5) 2x⁴ x 7y³ =
6) 6r⁴ x 2r x 4r² =
7) -5a⁴ x 4a² =
8)1/2a³ x 1/2a² =
9) 2x²y⁴ x 3x³y² x xy =
10) 0.3m⁴ x 0.3m x -0.3m² =
answers: 1) x⁹ 2) p⁸ 3) w¹º 4) 18y⁹ 5) 14x⁴y³ 6) 48r⁷ 7) -20a⁶ 8) 1/4a⁵ 9) 6x⁶y⁷ 10) -0.027m⁷
DIVIDING INDICES
When multiplying indices with the same base SUBTRACT their powers
Example: x⁸ ÷ x² = x⁸/x² = x⁶ since 8 - 2 = 6
This is the same as : xxxxxxxx/xx = xxxxxx
Example with numbers and variables combined: 8x¹º ÷ 4x² = 2x⁸ since 8 ÷ 4 = 2 and 10 - 2 = 8
This can be expressed as a rule:
Example: x⁸ ÷ x² = x⁸/x² = x⁶ since 8 - 2 = 6
This is the same as : xxxxxxxx/xx = xxxxxx
Example with numbers and variables combined: 8x¹º ÷ 4x² = 2x⁸ since 8 ÷ 4 = 2 and 10 - 2 = 8
This can be expressed as a rule:
ACTIVITY 2
Simplify these expressions:
1) 10x⁶ ÷ 2x² =
2) 12x⁶ ÷ 6x⁵ =
3) 25x¹º/5x⁵=
4) 9ef⁶/3ef²=
5) 21p¹ºq⁴ ÷ 3p⁸q² =
ANSWERS: 1) 5x⁴ 2) 2x¹ =2x 3) 5x⁵ 4) 3f⁴ 5) 7p²q²
POWERS OF ZERO (SPECIAL CASE)
Any base to the power of zero is equal to 1
aº = 1
Example:
a²/a² = a² = a² - ² = aº
a²/a² also = 1
so aº = 1
aº = 1
Example:
a²/a² = a² = a² - ² = aº
a²/a² also = 1
so aº = 1
POWERS OF POWERS
The rule for taking the power of a power is: MULTIPLY the indices and is shown as
Notice the number 2 inside the bracket is also taken to the third power.
SQUARE ROOTS OF ALGEBRAIC EXPRESSIONS
Take the square root of the number and divide the index or power by 2
Examples:
Examples:
since 3x² x 3x² = 9x⁴
ACTIVITY 4
CUBE ROOTS OF ALGEBRAIC EXPRESSIONS
Take the cube root of the number and divide the index or power by 3
ACTIVITY 5: Mixture of indices
ANSWERS: