Question = Simplify a^{4} x a^{5}-------------------------------------------So here we have two 'groups' of a being multiplied together. We can rewrite a^{4} and a^{5} as the following:a^{4} = a x a x a x aa^{5} = a x a x a x a x aIf we substitute these into the original question we have:a^{4} x a^{5} = a x a x a x a x a x a x a x a x aIf we count these we have 9 lots of a multiplied together, so this can be rewritten as a^{9}.Notice that 4 + 5 = 9, so when we **multiply **two identical values or letters (these are sometimes called "variables") that are presented in index / power form, we can simply **add the powers together**.So, to conclude: a^{4}x a^{5} = a^{9}, which we can obtain from the techniques of multiplying indices.