Algebraic Roots & Indices (Edexcel IGCSE Maths A)

Flashcards

1/13

FrontAlgebraic Roots & Indices
Write down the index law for $a^{m} \times a^{n}$ .

Enjoying Flashcards?
Tell us what you think

Cards in this collection (13)

Write down the index law for $a^{m} \times a^{n}$ .
$a^{m} \times a^{n} = a^{m + n}$ .
You add the powers when multiplying two powers with the same base.
Write down the index law for $\frac{a^{m}}{a^{n}}$ .
$\frac{a^{m}}{a^{n}} = a^{m - n}$ .
You subtract the powers when dividing two powers with the same base.
Write down the index law for ${(a^{m})}^{n}$ .
${(a^{m})}^{n} = a^{m n}$ .
You multiply the powers when raising $a^{m}$ to the power $n$ .
Write down the index law for $a^{\frac{1}{m}}$ .
$a^{\frac{1}{m}} = \sqrt[m]{a}$ .
A fractional power of $\frac{1}{m}$ means the $m^{th}$ root.
Write down the index law for ${(a b)}^{n}$ .
${(a b)}^{n} = a^{n} b^{n}$ .
The power outside acts on every term inside, when the terms inside are multiplied together.
Write down the index law for $a^{- m}$ .
$a^{- m} = \frac{1}{a^{m}}$ .
A negative power means 1 over the positive power.
Write down the index law for $a^{1}$ .
$a^{1} = a$ .
Anything to the power 1 is itself.
Write down the index law for $a^{0}$ .
$a^{0} = 1$ .
Anything to the power 0 is 1.
True or False?
$a^{\frac{m}{n}} = \sqrt[m]{a^{n}}$
False.
The order of $m$ and $n$ are incorrect.
The correct index law is $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ .
True or False?
$a^{\frac{m}{n}}$ can be thought of in two different ways, using powers and roots.
True.
You can swap the order of the $n^{th}$ root and the power of $m$ .
So $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$ is the first way to think about it, and $a^{\frac{m}{n}} = {(\sqrt[n]{a})}^{m}$ is the second way to think about it.
When talking about indices, what is the base?
The base is the number or letter being acted on by the power. For example, in $a^{n}$ , the base is $a$ and the power is $n$ .
What is the first step to solving the equation $3^{x} = 27^{x + 1}$ ?
You need both sides to be over the same base. So your first step is to change the base of 27 to 3, using the fact that 27 = 3³ (or change the base of 3 to 27, using the fact that $3 = 27^{\frac{1}{3}}$ ).
True or False?
${(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}$
True.
A fraction to a negative power is the same as the flipped fraction to the positive power, ${(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}$ . This is a great trick to use in exams!

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability