Standard Form of an Algebraic Expression

The standard form of an algebraic expression is a way to write an expression by arranging the terms in decreasing order of their exponents. The general form of a standard form expression is:

Ax^n + Bx^(n-1) + Cx^(n-2) + ... + Rx^2 + Sx + T

Where A, B, C, ..., R, S, T are constants and n is the highest exponent in the expression.

Example Expression

Let's consider the expression: -p'6 - 8p*9 + p*7 + 5

Step 1: Combine like terms
To simplify the expression, we need to combine the like terms. Like terms are the terms that have the same variable raised to the same exponent.

The given expression does not have any like terms, so we can skip this step.

Step 2: Arrange terms in decreasing order of exponents
To write the expression in standard form, we need to arrange the terms in decreasing order of their exponents.

The given expression can be rearranged as follows:

-8p*9 + p*7 - p'6 + 5

Step 3: Simplify the exponents
In the expression, we have exponents for the variables p. We need to simplify the exponents according to their rules.

The exponent p'6 means p^6 (p raised to the power of 6).
The exponent p*7 means p^7 (p raised to the power of 7).

After simplifying the exponents, our expression becomes:

-8p^9 + p^7 - p^6 + 5

Step 4: Write the expression in standard form
Now, we can write the expression in standard form by arranging the terms in decreasing order of their exponents:

-8p^9 + p^7 - p^6 + 5

This is the standard form of the given expression.

Summary

In summary, the standard form of an algebraic expression is a way to write an expression by arranging the terms in decreasing order of their exponents. To convert an expression into standard form, we need to combine like terms, arrange terms in decreasing order of exponents, simplify the exponents if necessary, and write the expression in the general form. In the given example, we rearranged the terms and simplified the exponents to write the expression -p'6 - 8p*9 + p*7 + 5 in standard form as -8p^9 + p^7 - p^6 + 5.