Simplify.
(i) (25×t⁻⁴)/(5⁻³×10×t⁻⁸) (t ≠ 0)
(ii) (3⁻⁵×10⁻⁵×125)/(5⁻⁷×6⁻⁵)

Solution:

The exponent of a number shows how many times the number is multiplied by itself.

(i) (25 × t⁻⁴)/(5⁻³ × 10 × t⁻⁸)

Let's express 25 and 10 in terms of their prime actors as shown below,

= (5² × t⁻⁴)/(5⁻³ × 5 × 2 × t⁻⁸ )

= (5² × t⁻⁴)/(5^{−3 + 1} × 2 × t⁻⁸) [Since, a^m × aⁿ = a^{m + n}]

= (5² × t⁻⁴)/(5⁻² × 2 × t⁻⁸)

= (5²⁻⁽⁻²⁾ × t^{−4−(−8)})/2 [Since, a^m/aⁿ = a^{m − n}]

= (5⁴ × t^{−4 + 8})/2

= 625t⁴/2

(ii) (3⁻⁵×10⁻⁵×125)/(5⁻⁷× 6⁻⁵)

Let's express 10, 6 and 125 in terms of their prime factors.

= (3⁻⁵ × (2 × 5)⁻⁵ × 5³)/(5⁻⁷× (2 × 3)^-5)

= 3^{−5−(−5)} × 2^{−5−(−5)} × 5^{−5−(−7)+3} [Since, a^m × aⁿ = a^{m + n} and a^m/aⁿ = a^{m − n}]

= 3⁰ × 2⁰ × 5⁵

= 1 × 1 × 5⁵ [∵a⁰=1]

= 5⁵

☛ Check: NCERT Solutions for Class 8 Maths Chapter 12

Video Solution:

Simplify. (i) (25×t⁻⁴)/(5⁻³×10×t⁻⁸) (t ≠ 0) (ii) (3⁻⁵×10⁻⁵×125)/(5⁻⁷×6⁻⁵)

Class 8 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 7

Summary:

The value of the following expressions (i) (25×t⁻⁴)/(5⁻³×10×t⁻⁸) (t ≠ 0) (ii) (3⁻⁵×10⁻⁵×125)/(5⁻⁷×6⁻⁵) are (i) 625t⁴/2 and (ii) 5⁵ respectively

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