Algebraic Roots & Indices (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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In the term $a^{n}$ , what are $a$ and $n$ called?
$a$ is the base, and $n$ is the index.
The index is also called the power or the exponent, and when it is a positive whole number it tells you how many times the base is multiplied by itself.
How do you simplify $(3 x^{7}) \times (6 x^{4})$ ?
Work out the number part and the letter part separately, then multiply the two results together.
Here $3 \times 6 = 18$ and $x^{7} \times x^{4} = x^{11}$ , so the answer is $18 x^{11}$ .
Complete the simplification by filling in the missing number and the missing index:
$\frac{6 x^{7}}{3 x^{4}} =______x^{______}$
The completed simplification is:
$\frac{6 x^{7}}{3 x^{4}} = 2 x^{3}$
The numbers are divided, giving $6 \div 3 = 2$ ; they are not subtracted.
True or False?
${(3 x^{7})}^{2}$ simplifies to $3 x^{14}$ .
False.
The power outside the bracket applies to the $3$ as well as to $x^{7}$ , so the $3$ is squared too:
${(3 x^{7})}^{2} = 3^{2} \times {(x^{7})}^{2} = 9 x^{14}$
Find the value of $x$ if $q^{x} = \frac{q^{2} \times q^{5}}{q^{10}}$ .
$x = - 3$ .
Simplify the right-hand side first so that it becomes a single power of $q$ : the numerator gives $q^{7}$ , and dividing that by $q^{10}$ leaves $q^{- 3}$ .

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