Exercise 11.1
Note: In most of the examples that we have taken in this chapter, the base of a power was taken an integer. But all the results of the chapter apply equally well to a base which is a rational number.
1. Write the base and the exponent in each case. Also, write the term in the expanded form.
Answer
(i)
(i)
Base :
Exponent :
Expanded form :
(ii)
(ii)
Coefficient :
Base :
Exponent:
Expanded form :
(iii)
(iii)
Base :
Exponent :
Expanded form :
(iv)
(iv)
Base :
Exponent :
Expanded form :
(2) Write the exponential form of each expression.
Answer
(i)
(i) 7 × 7 × 7 × 7 × 7
Exponential form : 7
(ii)
(ii) 3 × 3 × 3 × 5 × 5 × 5 × 5
Exponential form : 3
(iii)
(iii) 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5
Exponential form : 2
3. Express the following as the product of exponents through prime factorization.
Answer
(i)
(i) 288
Prime factorization : 2
(ii)
(ii) 1250
Prime factorization : 2 × 5
(iii)
(iii) 2250
Prime factorization : 2 × 3
(iv)
(iv) 3600
Prime factorization : 2
4. Identify the greater number in each of the following pairs.
Answer
(i)
(i)
Therefore,
(ii)
(ii)
Therefore,
(iii)
(iii)
Therefore,
5. If
Answer
(i)
(i)
First, let's substitute the values:
Now, let's calculate step by step:
(ii)
(ii)
First, let's substitute the values:
Now, let's calculate step by step:
(iii)
(iii)
First, let's substitute the values:
Now, let's calculate step by step:
(iv)
(iv)
First, let's substitute the values:
Now, let's calculate step by step: