Algebra ToolkitEdexcel IGCSE Maths: Flashcards

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What does $a^n$ mean?

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What does $a^n$ mean?: $a$ multiplied by itself $n$ times: $a \times a \times \dots \times a$ ( $n$ times)
What is $a^0$ (for $a \neq 0$ )?: $1$ — any non-zero number to the power 0 equals 1
What is $a^{-n}$ ?: $\dfrac{1}{a^n}$ — a negative index means 'one over' the positive power
What is $a^{\frac{1}{n}}$ ?: $\sqrt[n]{a}$ , the $n$ th root of $a$
Index law for $a^m \times a^n$ ?: $a^{m+n}$ — add the indices when multiplying (same base)
Index law for $a^m \div a^n$ ?: $a^{m-n}$ — subtract the indices when dividing (same base)
Index law for $(a^m)^n$ ?: $a^{mn}$ — multiply the indices for a power of a power
What is $a^{\frac{m}{n}}$ ?: $\left(\sqrt[n]{a}\right)^m$ — take the $n$ th root, then raise to the power $m$
Can you combine $x^3$ and $y^2$ using index laws?: No — the index laws only work when the bases are the same
What does BIDMAS stand for?: Brackets, Indices, Division/Multiplication, Addition/Subtraction — the order of operations
Why substitute negative numbers in brackets?: To avoid losing the minus sign or misapplying an index, e.g. $(-3)^2 = 9$ , not $-9$
What are 'like terms'?: Terms with identical letter parts raised to identical powers, e.g. $4x^2$ and $-7x^2$
Can $3x$ and $5x^2$ be combined into one term?: No — they have different powers of $x$ , so they are not like terms
Simplify $3x + 5x$: $8x$
Simplify $4x^2 + 3x - 2x^2 - 5x$: $2x^2 - 2x$