Question

Question: General form of algebraic function\[{x^5}\]multiply\[{x^1}\]have solved form as
A. \[{x^4}\]
B. 2\[{x^4}\]
C. \[{x^6}\]
D. 2\[{x^6}\]

Answer 1

Hint: The variables are the alphabets that can be used in the mathematics to assume the unknown fields or values. The value of the variable could be any integer (negative integer or positive or integer). Here in this solution, the variables are same and the powers are different, so remember the formulas of surds and indices and follow according to it.

Complete step-by-step answer:
The terms to be multiplied are\[{x^5} \times {x^1}\],
Then we know that according to the statements of surds and indices if the bases of any two terms are the same or similar then we can add their powers. So according to this statement the general form of the algebraic function is
\[{a^m} \times {a^n}\],
Here the bases are a and a (we can say variables also), the powers are m and n.
In the above terms, the bases (a and a in both terms) both are equal, so the powers m and n are indeed to add, then the general form will be
\[{a^m}^{ + n}\]
Therefore, the general form of algebraic function is\[{a^m}^{ + n}\].
According to the general form, the given terms can be solved as follows
\[{x^5} \times {x^1}\], her the bases (x and x in both terms) are same or similar, so the output will be
\[{x^5}^{ + 1} = {x^6}\]
Therefore, the value of the given terms is \[{x^6}\], it means the option (C) is correct.
So, the correct answer is “Option C”.

Note: Here, we may confuse when the powers should be added, but it should keep in mind that the two terms with powers and both are in a multiplication relation, then the powers of the two terms are eligible to add.