Use of exponents in algebra.

 Welcome friends!

              Uptil now we learnt that how to Add or Subtract two or more

 Algebraic Expression. Before going for multiplication in algebraic

 expression (polynomial) we must learn the use of exponents in Algebra. 

As in multiplication we are going to multiply the variables with exponents.

What is a variable with an exponent?

• ·        Variable is a symbol for a number we don’t know yet. It is usually a letter.
• ·    An exponent says how many times to use the variable in multiplication.

What is the meaning of x⁵?

This means the x is multiplied with itself 5 times.

Here, X – Base of exponential term

         5 – Exponent / Power / Index (indicate how many times x is multiplied to itself)

In General

Benefits of using exponents

·        It is easy to read and write.

·        It is easy to calculate. (with the help of law of exponents)

Negative Exponents

Vice-versa

Means sign in exponent indicates where to move the exponent (in

 numerator or denominator) of a fraction by simply changing the sign of 

the exponent.

Positive and Negative exponents together:

Exponents of 1 and 0

Exponent of 1

When the exponent is 1, means the variable itself (x¹=x)

(Normally, we don’t write the 1 in power but it is better to remember

 that x is also X¹.)

Exponent of 0

When the exponent is 0, we are not multiplying by anything and the

 answer is just “1”. (Ex. X⁰=1, Y⁰=1, etc).

But,

Multiplying variable with exponents:

Let us see an example

Note: here, base is same & operation between them is multiplication,

 but for different base it won’t work & this is one of the laws of 

exponents.

Multiplication when mixed variable:

Let us see the example

Multiplication when having constant:

            Sometimes along with exponential variable constants appears that

 time follow the following method shown in example.

How to deal with Negative exponents

  

Dividing

We can do this by using laws of exponents

So, just subtract the exponent when division is there & the base is same.

Take some complicated examples:

Problems for Practice:

1) (2x⁴y²)(3y³)

2) (6y⁵z³)¸ (3y²z²)

3) (3a⁶b⁵)(5a²bc³)

4) (25x⁴y⁴z²) ¸ (5xy²z)

5) [(8x³y)(2xy⁶)] ¸ (4x²y³)

This is all!

Thank you!

Hope you may learn how to use exponents in multiplication here.

you may visit also:

Introduction to algebra ( Part I)

Introduction to Algebra (Part II)

Transposing Method of Solving Algebra

Order of Operations – BODMAS/PEMDAS

Algebra - Substitution

Introduction to Inequalities in Algebra

Introduction to Algebraic Expression.

Introduction to Addition & Subtraction of Algebraic Expression (Polynomial)

Degree of an Expression (Polynomial)