### Exercise-13.1

Question 1:

Find the value of:

(i) 2^{6}

(ii) 9^{3}

(iii) 11^{2}

(iv) 5^{4}

Answer:

(i)In the given question,

We have to find the value of 26

We have,

26 = 2 × 2 × 2 × 2 × 2 × 2= 64

(ii) In the given question,

We have to find the value of 93

We have,

93 = 9 × 9 × 9 = 729

(iii) In the given question,

We have to find the value of 112

We have,

112 = 11 × 11 = 121

(iv) In the given question,

We have to find the value of 54

We have,

54 = 5 × 5 × 5 × 5= 625

Question 2:

Express the following in exponential form:

(i) 6 × 6 × 6 × 6

(ii) t × t

(iii) b × b × b × b

(iv) 5 × 5 × 7 × 7 × 7

(v) 2 × 2 × a × a

(vi) a × a × a × c × c × c × d

Answer:

(i) In the given question,

We have to express the given expression into exponential form

We have,

6 × 6 × 6 × 6 = 64

(ii) In the given question,

We have to express the given expression into exponential form

We have,

t × t = t2

(iii) In the given question,

We have to express the given expression into exponential form

We have,

b × b × b × b = b4

(iv) In the given question,

We have to express the given expression into exponential form

We have,

5 × 5 × 7 × 7 × 7 = 52 × 73

(v) In the given question,

We have to express the given expression into exponential form

We have,

2 × 2 × a × a = 22 × a2

(vi) In the given question,

We have to express the given expression into exponential form

We have,

a × a × a × c × c × c × c × d = a3 × c4 × d

Question 3:

Express each of the following numbers using the exponential notation:

(i) 512

(ii) 343

(iii) 729

(iv) 3125

Answer:

(i) In the given question,

We have to express the given numbers into exponential notation

We have,

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 29

(ii) In the given question,

We have to express the given numbers into exponential notation

We have,

343 = 7 × 7 × 7 = 73

(iii) In the given question,

We have to express the given numbers into exponential notation

We have,

729 = 3 × 3 × 3 × 3 × 3 × 3 = 36

(iv) In the given question,

We have to express the given numbers into exponential notation

We have,

3125 = 5 × 5 × 5 × 5 × 5 = 55

Question 4:

Identify the greater number, wherever possible, in each of the following.

### Exercise-13.2

**Question 1:**

Using laws of exponents simplify and write the answer in exponential form:

(i) 3^{2} × 3^{4} × 3^{8}

(ii)

(iii) **a**** ^{3 }**× a

^{2}

(iv) **7**^{x} × 7^{2}

(v)

(vi**)2**^{5} × 5^{2}

(vii)**a**^{4} × b^{4}

(viii)(3^{4})^{3}

(ix)

(x)

**Answer:**

(i) We have,

3^{2}× 3^{4} × 3^{8}

We know that,

(a^{m}× a^{n} = a^{m + n})

Thus,

3^{2}× 3^{4} × 3^{8}

= (3)^{2 + 4 + 8}

= 3^{14}

(ii) We have,

6^{15} 6^{10}

We know that,

(a^{m} a^{n} = a^{m – n})

Thus,

6^{15} 6^{10}

= (6)^{15 – 10}

= 6^{5}

(iii) We have,

a^{3}× a^{2}

We know that,

(a^{m}× a^{n} = a^{m + n})

Therefore,

a^{3}× a^{2}

= (a)^{3 + 2}

= a^{5}

(iv) We have,

7^{x} × 7^{2}

We know that,

(a^{m} × a^{n} = a^{m + n})

Thus,

7^{x} × 7^{2}

= (7)^{x + 2}

(v) We have,

(5^{2})^{3} 5^{3}

Using identity:

(a^{m})^{n}= a^{m} × n

= 5^{2 × 3} 5^{3}

= 5^{6} 5^{3}

We know that,

(a^{m} a^{n} = a^{m – n})

Thus,

5^{6} 5^{3}

= (5)^{6 – 3}

= 5^{3}

(vi) We have,

2^{5}× 5^{5}

We know that,

[a^{m} ×b^{m} = (a × b)^{m}]

Thus,

2^{5}× 5^{5}

= (2 × 5)^{5 + 5}

= 10^{5}

(vii) We have,

a^{4} × b^{4}

We know that,

[a^{m} × b^{m} = (a × b)^{m]}

Thus,

a^{4} × b^{4}

= (a × b)^{4}

(viii) We have,

(3^{4})^{3}

We know that,

(a^{m})n = a^{mn})

Thus,

(3^{4})^{3}

= (3^{4})^{3}

= 3^{12}

(ix) We have,

(2^{20} 2^{15}) × 2^{3}

We know that,

(a^{m} a^{n} = a^{m – n})

Thus,

(2^{20 – 15}) × 2^{3}

= (2)^{5 }× 2^{3}

We know that,

(a^{m} × a^{n} = a^{m + n})

Thus,

(2)^{5 }× 2^{3}

=(2^{5 + 3})

= 2^{8}

(x) We have,

(8^{t} 8^{2})

We know that,

(a^{m} a^{n} = a^{m – n})

Thus,

(8^{t} 8^{2})

= (8^{t – 2})