RS Aggarwal Solutions Class 7 Maths Chapter 5 Ex 5.1: Class 7 Maths is made easier, all thanks to RS Aggarwal Solutions Class 7 Maths. The subject matter experts believe in clearing all your doubts and that’s why the solutions of RS Aggarwal Solutions Class 7 Maths Chapter 5 Ex 5.1 are well-explained and accurate.
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RS Aggarwal Solutions Class 7 Maths Chapter 5 Ex 5.1
RS Aggarwal Solutions Class 7 Maths Chapter 5 Ex 5.1 – Overview
Exponents And Powers
The exponents and powers are generally used to represent the big amount of data or the small amount of data’s in a very easy and human-understandable form.
Eg: We can represent the number 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 in its simplest and understanding form as 48. Here, 4 is the base value and 8 is the exponent value.
This expression 48 here is the power value. Henceforth, the value of the exponent will be dependent on the total number of times the base value is multiplied by itself.
Any particular number, ‘x’ raised to the power ‘y’ is expressive in the above form where ‘x’ is any non zero number and the ‘y’ is a natural number.
We can also call this expression ‘xy’ as the yth power of x. Here,
‘x’ is the base value and ‘y’ can be said to be the index value or exponent value or the power value.
So, this ‘x’ is multiplied ‘y’ number of times. And this method is also called the shorthand method for the repeated multiplication.
Laws Of Exponents
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Multiplication Law Of Exponents
According to this law, the product down between the two exponents having the same base value along with the different power values is equivalent to the base value raised to the addition of these two power values.
Here the similar values are multiplied while adding the exponents and keeping the base exactly the same.
Ideally, xy × xz = xy + z
- Division Law Of Exponents
While dividing the two exponents with the same base values but the different power values, in this case, it will result in the base value which is being raised to the difference in between the two power values.
xy ÷ xz = xy / xz = xy raised to the power -z
Negative Exponent Law
If any base is having a negative power, in this case, it will result in the reciprocal of it having the positive power value or the integer value to its base value.
x-y = 1 / xy
Rules
We have certain laws of exponents apart from the rules that need to be followed up while working on any given problem.
Let us take “w and x” as the integer numbers and “y and z” as the power values and express the rules and laws on the form given below.
1. x0 = 1
As per the standard law, of exponents and the powers, if the power of any random integer is equivalent to the number ‘zero’, in this case, the output yield will be either unity or 1.
Eg: 40 = 1
Here, the number ‘4’ raised to the power 0 is equivalent to 1.
2. ( xy ) z = x ( yz )
The ‘x’ is being raised to the power value of ‘y’ which as a whole is multiplied with the power value of ‘z’. This entire expression as a whole is equivalent to the ‘x’ which is being raised to the power product of ‘y’ and ‘z’.
Eg: ( 32 ) 4 = 3 (2×4)
3. wy × xy = ( wx ) y
The product of ‘w’ which is being raised to the power value of ‘y’ is being done with the ‘x’ which is raised to the power value of ‘y’. It is equivalent to the production values of ‘w’ and ‘x’ which as a whole is raised to the power value of ‘y’.
Eg: 32 × 12 =( 3 x 1 ) 2
4. wy / xy = ( w / x ) y
The division of ‘w’ which is raised to the power value of ‘y’ is done with the ‘x’ raised to the power value of ‘y’ will be equivalent to the division of ‘w’ done with the ‘x’ where this entire expression is raised to the power ‘y’.
Eg: 42 / 52 = ( 4 / 5) 2
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Define Division Law OF Exponents.
While dividing the two exponents with the same base values but the different power values, in this case, it will result in the base value which is being raised to the difference in between the two power values.
xy ÷ xz = xy / xz = xy raised to the power -z
Define Multiplication Law OF Exponents.
According to this law, the product down between the two exponents having the same base value along with the different power values is equivalent to the base value raised to the addition of these two power values.
Here the similar values are multiplied while adding the exponents and keeping the base exactly the same.
Ideally, xy × xz = xy + z