1. Write an R program that generates a limited exponents chart for 3, 4, and 5 (powers of 3, powers of 4,and powers of 5) and perform some calculations.

   
   

   1. Write the function powerSeq(base, maxExp) which:

   a. returns a finite sequence (named vector) of a given number (base) raised to incrementing powers starting with (base)0. For instance, (base)0,(base)1,(base)2,(base)3,(base)4,(base)5.

   b. accepts two arguments base and maxExp, where base is the integer base and maxExp is the maximum exponent of the sequence.

   c. verifies that base and maxExp are integers.

   d. names the components of the returned vector by their exponent value (e.g., the component base0 is named 0, and base1 is named 1).

   
   

   2. Use powerSeq(base, maxExp) and generate 3 named vectors representing the sequential powers from 0 to 10 of 3, 4, and 5 (e.g., 30, 31, 32, 33,...310).

   
   

   3. Combine the 3 vectors (powers of 3, powers of 4, and powers of 5) into a matrix (powerChart) by column. Rename the columns to 3, 4, and 5; Ensure that the rows still carry the

   exponent-based names.

   
   

   4. Generate a new matrix (powerChartDes) that resembles powerChart but offers a readable notation in such a way that each component of powerChart now reads (base) to the power of (exponent) = (value), where base is the column name, exponent is the row name of the given component, and value is base(exponent). For instance, the component with the value 243 in powerChart shall be “3 to the power of 5 = 243” in powerChartDes.

   
   

   5. x−n=1/xn . Generate a new matrix (negPowerChart) for the negative powers of 3, negative powers of 4, and negative powers of 5 by using powerChart.

   6. Using powerChart, generate a sequence (vector) of 10 components where each component C is given by the fuction:

   a. Cn= 3n + 5n – 4n (n = 0, 1, 2, 3...10).