M - Pure 1 - 1) Algebraic expressions

Question 1

List of all index laws

Answer 1

• a^m × aⁿ = a^{m + n}
• a^m ÷ aⁿ = a^{m - n}
• (a^m)ⁿ = a^mn
• (ab)ⁿ = aⁿ·bⁿ
• a^n/m = ^m√aⁿ
• a^-m = 1/a^m
• a⁰ = 1

Question 2

Equation for difference of two squares

Answer 2

x² - y² = (x + y)(x - y)

Question 3

Manipulate √ab and √a/b

Answer 3

• √a × √b
• √a/√b

Question 4

Ways to rationalise 1/√a, 1/[a + √b] and 1/[a - √b]

Answer 4

Multiply numerator and denominator by:

• √a
• a - √b
• a + √b