NCERT Solutions class 7 Maths Chapter-13 Exercise 13.2

NCERT Solutions class 7 Maths Chapter-13 Exercise 13.2

NCERT Solutions class 7 Maths Chapter-13 Exponents and Powers

Exponents and Powers Exercise-13.2

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Solutions of Chapter  Exponents and Powers  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} )

NCERT CLASS 7 MATHEMATICS SOLUTIONS