4. Powers | root power
OnthispageRelatedSectionDon’tmissthechapterExponentsandRadicals[1],wherewegointomoredetailonthesetopics.Onthispage,we’llcontinuetorevisehownumberswork,beforeapplyingtheprocedurestoalgebra.Itallworksthesame,exceptthatinalgebraweuseletterstostandfornumbers.IndicesIndices(orpowers,orexponents)areveryusefulinmathematics.Indicesareaconvenientwayofwritingmultiplicationsthathavemanyrepeatedterms.ExampleofanIndexFortheexample53,wesaythat:5isthebaseand3istheindex(orpower,orexponent).53means"multiply5...
On this page Related SectionDon’t miss the chapter Exponents and Radicals[1], where we go into more detail on these topics.
On this page, we’ll continue to revise how numbers work, before applying the procedures to algebra. It all works the same, except that in algebra we use letters to stand for numbers.
IndicesIndices (or powers, or exponents) are very useful in mathematics. Indices are a convenient way of writing multiplications that have many repeated terms.
Example of an IndexFor the example 53, we say that:
5 is the base and
3 is the index (or power, or exponent).
53 means "multiply 5 by itself 3 times".
[Or more accurately, "multiply 5 by itself repeatedly such that there are three 5’s in the multiplication", or even better, "three 5’s multiplied together". See a discussion on this at Stumbling blocks in math[2].]
That is, 53 means
53 = 5 × 5 × 5
Examples of Intege...