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) 3² × 3⁴ × 3⁸

(ii)

(iii)  a³  × a²

(iv) 7^x × 7²

(v)        

(vi)2⁵ × 5²

(vii)a⁴ × b⁴

(viii)(3⁴)³

(ix)

(x)

Answer:

(i) We have,

3²× 3⁴ × 3⁸

We know that,

(a^m× aⁿ = a^{m + n})

Thus,

3²× 3⁴ × 3⁸

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

= 3¹⁴

(ii) We have,

6¹⁵ 6¹⁰

We know that,

(a^m aⁿ = a^{m - n})

Thus,

6¹⁵ 6¹⁰

= (6)^{15 - 10}

= 6⁵

(iii) We have,

a³× a²

We know that,

(a^m× aⁿ = a^{m + n})

Therefore,

a³× a²

= (a)^{3 + 2}

= a⁵

(iv) We have,

7^x × 7²

We know that,

(a^m × aⁿ = a^{m + n})

Thus,

7^x × 7²

= (7)^{x + 2}

(v) We have,

(5²)³ 5³

Using identity:

(a^m)ⁿ= a^m × n

= 5^{2 × 3} 5³

= 5⁶ 5³

We know that,

(a^m aⁿ = a^{m - n})

Thus,

5⁶ 5³

= (5)^{6 - 3}

= 5³

(vi) We have,

2⁵× 5⁵

We know that,

[a^m ×b^m = (a × b)^m]

Thus,

2⁵× 5⁵

= (2 × 5)^{5 + 5}

= 10⁵

(vii) We have,

a⁴ × b⁴

We know that,

[a^m × b^m = (a × b)^m]

Thus,

a⁴ × b⁴

= (a × b)⁴

(viii) We have,

(3⁴)³

We know that,

(a^m)n = a^mn)

Thus,

(3⁴)³

= (3⁴)³

= 3¹²

(ix) We have,

(2²⁰ 2¹⁵) × 2³

We know that,

(a^m aⁿ = a^{m - n})

Thus,

(2^{20 - 15}) × 2³

= (2)⁵ × 2³

We know that,

(a^m × aⁿ = a^{m + n})

Thus,

(2)⁵ × 2³

=(2^{5 + 3})

= 2⁸

(x) We have,

(8^t 8²)

We know that,

(a^m aⁿ = a^{m - n})

Thus,

(8^t 8²)

= (8^{t – 2})

NCERT CLASS 7 MATHEMATICS SOLUTIONS