OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6. We Provide Step by Step Answer of Exe-6(a), Exe-6(b), Exe-6(c), Exe-6(d), with Chapter Test of S Chand OP Malhotra Maths . Visit official Website CISCE for detail information about ICSE Board Class-9.
OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
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Exercise-6
OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
Index Definition :
A number or a variable may have an index. Index of a variable (or a constant) is a value that is raised to the power of the variable. The indices are also known as powers or exponents. It shows the number of times a given number has to be multiplied. It is represented in the form:
| am = a × a × a ×……× a (m times) |
Here, a is the base and m is the index.
The index says that a particular number (or base) is to be multiplied by itself, the number of times equal to the index raised to it. It is a compressed method of writing big numbers and calculations.
Example: 23 = 2 × 2 × 2 = 8
In the example, 2 is the base and 3 is the index.
Laws of Indices :
There are some fundamental rules or laws of indices which are necessary to understand before we start dealing with indices. These laws are used while performing algebraic operations on indices and while solving the algebraic expressions, including it.
Rule 1: If a constant or variable has index as ‘0’, then the result will be equal to one, regardless of any base value.
| a0 = 1 |
Laws of Exponents :
The laws of exponents are demonstrated based on the powers they carry.
- Bases – multiplying the like ones – add the exponents and keep the base same. (Multiplication Law)
- Bases – raise it with power to another – multiply the exponents and keep the base same.
- Bases – dividing the like ones – ‘Numerator Exponent – Denominator Exponent’ and keep the base same. (Division Law)
Let ‘a’ is any number or integer (positive or negative) and ‘m’, ‘n’ are positive integers, denoting the power to the bases, then;
Multiplication Law :
As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers.
am × an = am+n
Division Law :
When two exponents having same bases and different powers are divided, then it results in base raised to the difference between the two powers.
am ÷ an = am / an = am-n
Negative exponents :
Exercise-6.(a)
OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
Question 1:
Write the product in the exponential form
(i)………….
(ii)……….
(iii)……….
(iv)………..
Question 2:
Write each expression in the simpler form :
(i)………….
(ii)……….
(iii)……….
(iv)………..
(v)………….
(vi)……….
(vii)……….
(viii)………..
(ix)………….
(x)……….
(xi)……….
(xii)………..
Exercise-6.(b)
OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
Question 1:
Evaluate :
(i)………….
(ii)……….
(iii)……….
(iv)………..
(v)………….
(vi)……….
(vii)……….
(viii)………..
(ix)………….
Question 2:
Evaluate :
(i)………….
(ii)……….
(iii)……….
(iv)………..
(v)………….
(vi)……….
(vii)……….
(viii)………..
(ix)………….
(x)……….
(xi)……….
(xii)………..
Exercise-6.(c)
Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
Question 1:
Evaluate :
(i)………….
(ii)……….
(iii)……….
(iv)………..
(v)………….
Question 2:
………………..
………………….
…………………
Question 8:
Prove that ………
…………………….
…………………..
Question 10:
If ……………………… prove that x = ………..
Question 11:
If x = ab ……………….. =1
Exercise-6.(d)
OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
Solve the following equations :
Question 1:
2 ………………
…………………..
……………………
Question 16:
2 …………………..
…………………..
………………….
Chapter Test
OP Malhotra Indices or Exponents Class-9 S.Chand ICSE Maths Ch-6
Question 1:
Determine whether each equation is true or false. Change the right side of the equations to make a true equation.
(i)………….
(ii)……….
(iii)……….
(iv)………..
Question 2:
………………….
…………………..
………………………
Question 10:
(i) solve : ……………..
(ii) ……………….
— : End of Indices or Exponents OP Malhotra S Chand Solutions :–
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