Question

How do you perform addition, subtraction, multiplication, division, and exponentiation of arrays?

a) Using loops
b) Using functions
c) Using matrix operations
d) Using recursion

Answer 1

In arithmetic and programming, array operations can be performed using loops, functions, matrix operations, or even recursion. The rules for dealing with exponents include multiplying the exponents when raising a power to another power, adding exponents when multiplying like bases, and subtracting exponents when dividing like bases.

Step-by-step explanation:

Performing addition, subtraction, multiplication, division, and exponentiation of arrays can be approached in multiple ways, such as:

• Using loops by iterating through the elements of the arrays and performing the operations element-wise.
• Using functions that are built into programming languages or math libraries to handle these operations more directly on arrays.
• Using matrix operations particularly for multiplication and division, where array elements align with matrix concepts.
• Using recursion, which is a less common approach for array operations but can be used for processes like exponentiation.

Rules for Dealing with Exponents:

There are several rules for handling exponents which include: raising a power to another power, multiplying exponents, and dividing exponents. When you raise an exponent to another power, you multiply the exponents. For example,
`(a^m)^n = a^(mn)` multiply two exponentiated numbers with the same base, you add the exponents. For example,
`a^m * a^n = a^((m+n))` exponentiated numbers with the same base, you subtract the exponents.

For example,
`a^m / a^n = a^((m-n))` cvert an exponent, you change the sign of the exponent.

For example,
`(a^m)^-1 = a^(-m)` or
`1/a^m`