The exponents of a number says how many times to use the number in a multiplication.
for example 5³ = 5 x 5 x 5
In words 5³ could be called as 5 to the power 3 or 5 cube.
10² is called as 10 to the power 2 or simply called as 10 square. | |
10³ is called as 10 to the power 3 or simply called as 10 cube. | |
If we have 1/2 in the power, we can simply write the base inside the radical or square root. If we have 1/3 in the power,we can simply write the base inside the cube root |
If the power goes from one side of equal sign to the other side, it will flip. that is x = 4² |
The other names of exponent are index and power.
Rule 1: | |
When we have to simplify two or more the terms which are multiplying with the 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: | |
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 then we have to distribute the powers which are multiplying or dividing inside the bracket. Note : This rule is not applicable when two are more terms which are adding and subtracting. For example (x + y) ^m = (x^m + y^m) is not correct |
Other things:
Point 1 :
If we don't have any number in the power then we have to consider that there is 1
Point 2 :
In case we have negative power for any fraction and if we want to make it as positive,we can write the power as positive and we should write its reciprocal only. For example
Question 1 :
Simplify 4 x ^(-1)/x^(-1/3)
Solution :
Question 2 : Find the value of 2(256) ^(-1/8) Solution : = 2 (2^8)^(-1/8) = 2 (2^-1) = 2/2 = 1 |
Question 3 :
Find the value of
Question 4 :
Find the value of x^(a - b) x^(b - c) x^(c - a)
Solution :
Question 5 :
Find the value of (8/27)^(-1/3) (32/243)^(-1/5)
Solution :
After having gone through the stuff given above, we hope that the students would have understood "Exponents and powers".
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