About "Understanding exponents"

Understanding exponents :

Exponent says that how many times do we have to multiply the base by itself.

For example, let us consider 

 2³ =  2 x 2 x 2 (we multiply the base "2" three times)

Before going to see example based on the above concept, we have to know about two terms

(i) Base  

(ii) Exponent (or) power (or) index

How to read ?

We have to read the above question as 5 raised to the power 3, (or) 5 cube.

Example 1 :

Write the number 128 as the power of 2 

Solution :

To write the number 128 as the power of 2, we have to split the number 128 using 2 times table.

128  =  2 x 2 x 2 x 2 x 2 x 2 x 2

Since 2 is repeating 7 times, we have to write 2⁷.  

Basic rules in exponents

Rule 1:

When we have to simplify two or more the terms which are multiplying with same base,then we have to put the same base and add the powers. 

Rule 2 :

Whenever we have two terms which are diving with the same base,we have to put only one base and we have to subtract the powers.

Rule 3 :

Whenever we have power to the power, we have to multiply both powers. 

Rule 4 :

Anything to the power zero is 1.

Rule 5 :

If we have same power for 2 or more terms which are multiplying or dividing,we have to apply the powers for every terms.

Exponents with negative powers

Whenever we have a negative number as exponent and we need to make it as positive,we have to flip the base that is write the reciprocal of the base and we can change the negative exponent as positive exponent.

Fractions with negative exponents

Let us see some examples based on the above concepts.

Example 2 :

If 2^p = 32, find the value of p.

Solution :

To find the value of which is in he power, we have to write the number 32 as the multiples of 2.

2^p  =  2 x 2 x 2 x 2 x 2

Since 2 is repeating five times, we have to write 2 x 2 x 2 x 2 x 2 as 2^5

2^p  =  2

Since the bases are equal, we can say the powers are also equal.

p  =  5

Example 3 :

Simplify (2 x 3)

Solution :

(2 x 3)⁴  =  6

Since the power is 4, we have to multiply 6 four times.

  =  6 x 6 x 6 x 6

  =  1296

Example 4 :

Solution :

[(2/8)^2x] x [(2/8)^x]  =  [(2/8)^6]  

(2/8)^(2x + x)  =  (2/8)^6

(2/8)^(3x)  =  (2/8)^6

Since the bases are equal on both sides, we can equal the powers.

3x  =  6

x  =  6/3

x  =  2

Example 5 :


Solution :

Combining the terms which are having same base.

After having gone through the stuff given above, we hope that the students would have understood "Understanding exponents". 

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