Questions and Answers
What does the index law state for multiplication of exponents?
What is the value of m^0?
1
What does m^-1 equal?
1/m
The expression 2/(8x-y)^5 can be written as 2(8x-y)^5.
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What is the relationship expressed in fractional indices?
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Write in surd form: m^2/3.
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Write √2m in index form.
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The formula for the difference of two squares is a^2 - b^2 = ______
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What is factorisation (HCF)?
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What does 'trinomials' refer to?
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What is meant by 'rationalising the denominator'?
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Study Notes
Index Laws
- m^a x m^b results in m^(a+b)
- m^a ÷ m^b results in m^(a-b)
Zero Indices
- Any base raised to the power of zero equals one: m^0 = 1
Negative Indices
- m^-1 is equivalent to 1/m
- To express a negative exponent in a fraction, flip the fraction to make it positive, e.g., (2/3)^-1 = 3/2
Expressions with Negative Indices
- An expression like 2/(8x - y)^5 can be rewritten as 2(8x - y)^-5
Fractional Indices
- The expression √m multiplied by itself equals m
- m^(1/2) multiplied by m^(1/2) also equals m, establishing that √m = m^(1/2)
- The cube root of m, 3√m, multiplied by itself three times also equals m; therefore, 3√m = m
Writing in Surd Form
- The expression m^(2/3) can be expressed as the cube root of m squared: 3√(m^2)
Writing in Index Form
- The square root of 2m can be denoted as 2m^(1/2)
Factorisation (HCF)
- Revisiting factorisation methods is essential; concepts are usually straightforward.
Grouping in Pairs
- Practice problems related to grouping in pairs to enhance understanding.
Trinomials
- Trinomials can be transformed into bracketed equations, facilitating easier factorisation.
Perfect Squares
- Review perfect squares to strengthen algebraic manipulation skills.
Difference of Two Squares
- The formula a^2 - b^2 factors into (a+b)(a-b), a crucial algebraic identity to remember.
Algebraic Fractions
- Go through related questions to gain a better grasp of simplifying and manipulating algebraic fractions.
Simplifying Surds
- Practice examples focused on simplifying surds, reinforcing techniques learned.
Rationalising the Denominator
- It's crucial to fully revise methods of rationalising denominators to eliminate roots from the bottom of fractions.
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Description
This quiz consists of flashcards covering essential algebraic techniques, specifically index laws, zero, negative, and fractional indices. Each card provides a definition and examples to help reinforce your understanding of these concepts. Test your knowledge and master the fundamentals of algebra.