# Algebra Multiplication Rules

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There are some algebra multiplication rules of algebraic expressions that help in simplifying the equations clearly without any errors or wrong results. Following, implementing and practicing them on different types of questions helps in achieving mastery over the topic. We shall learn the most important rules that are must be known for solving problems.

## Basic Algebra Multiplication Rules Involved In Every Algebraic Equations

Here are the basic rules of how the signs are considered in multiplying algebraic expressions. These signs concept comes in every simplification. Remembering these 4 sign rules of multiplication helps in solving every algebraic expression.

### Sign Rule Multiplication In Algebra

 –     ×      –      =      + +      ×      +      =      + –      ×      +      =      – +      ×      –      =      –

### Examples for Multiplication Rules Of Algebraic Equations

Multiply the algebraic expressions -ax and -by
Sol:

(-ax) × (-by)
first, multiply the signs – × – = + and then coefficients and variables
+(abxy)

Multiply the algebraic expressions -ax and +by
Sol:

(-ax) × (+by)
first, multiply the signs – × + = – and then coefficients and variables
-(abxy)

### Rules Of Exponents Or Powers

Exponent or Power is defined as the number of times a number is multiplied by itself.

1. When bases are same in multiplication we add the powers
\begin{align*} a^{m}\times a^{n}=a^{m+n} \end{align*}
2. When bases are same in division we subtract the numerator power with denominator.
\begin{align*} \begin{aligned}\dfrac {a^{m}}{a^{n}}=a^{m-n}\\ where \ a\neq 0,m >n\end{aligned}
\end{align*}
3. For same base if there are one or more exponents then, multiply all the exponents.
\begin{align*} \left( a^{m}\right) ^{n}=a^{mn} \end{align*}
4. If exponents are same and bases are different then multiply the bases for same exponents.
\begin{align*} a^{m}\times b^{m}=\left( ab\right) ^{m} \end{align*}
5. When exponents are same in division with different bases then divide the bases with same exponent.
\begin{align*} \dfrac {a^{m}}{b^{m}}=\left( \dfrac {a}{b}\right) ^{m} \end{align*}
6. For any value of base if power is zero then the total value is always ‘1’.
\begin{align*} a^{0}=1 \end{align*}
7. Negative power can also be represented in denominator with positive power in fraction form.
\begin{align*} \begin{aligned}a^{-m}=\dfrac {1}{a^{m}}\\ a\neq 0\end{aligned} \end{align*}