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Evaluate : (7⁸×a¹⁰b⁷c¹²)/(7⁶×a⁸b⁴c¹²)

Solution:

Given, the expression is (7⁸ × a¹⁰b⁷c¹²)/(7⁶ × a⁸b⁴c¹²)

We have to evaluate the expression.

(7⁸ × a¹⁰b⁷c¹²)/(7⁶ × a⁸b⁴c¹²) = (7⁸/7⁶) × (a¹⁰/a⁸) × (b⁷/b⁴) × (c¹²/c¹²)

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m ÷ aⁿ = a^{m - n}

Considering 7⁸/7⁶,

Here, a = 7, m = 8 and n = 6

m - n = 8 - 6 = 2

7⁸/7⁶ = 7²

= 7 × 7

= 49

Considering a¹⁰/a⁸,

Here, m = 10 and n = 8

m - n = 10 - 8 = 2

a¹⁰/a⁸ = a²

Considering b⁷/b⁴,

Here, a = b, m = 7 and n = 4

m - n = 7 - 4 = 3

b⁷/b⁴ = b³

Considering c¹²/c¹²,

Here, a = c, m = 12 and n = 12

m - n = 12 - 12 = 0

c¹²/c¹² = c⁰

We know a^⁰ = 1

So, c⁰ = 1

Now, c¹²/c¹² = 1

So, (7⁸/7⁶) × (a¹⁰/a⁸) × (b⁷/b⁴) × (c¹²/c¹²) = 49 × a² × b³ × 1

Therefore, (7⁸ × a¹⁰b⁷c¹²)/(7⁶ × a⁸b⁴c¹²) = 49a²b³

✦ Try This: Evaluate : (9² × a⁸b⁵c²)/(3² × a⁵b²c)

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 85 (a)

Summary:

On evaluating (7⁸ × a¹⁰b⁷c¹²)/(7⁶ × a⁸b⁴c¹²) we get 49a²b³.

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