Simplify: (3⁻²)² × (5²)⁻³ × (t⁻³)² / (3⁻²)⁵ × (5³)⁻² × (t⁻⁴)³

Solution:

Given, the expression is (3⁻²)² × (5²)⁻³ × (t⁻³)² / (3⁻²)⁵ × (5³)⁻² × (t⁻⁴)³

We have to simplify the expression.

Using the law of exponents,

(a^m)ⁿ = a^mn

(3⁻²)² × (5²)⁻³ × (t⁻³)² / (3⁻²)⁵ × (5³)⁻² × (t⁻⁴)³ = 3⁻⁴ × 5⁻⁶ × t⁻⁶ / 3⁻¹⁰ × 5⁻⁶ × t⁻¹²

= 3⁻⁴/3⁻¹⁰ × 5⁻⁶/5⁻⁶ × t⁻⁶/t⁻¹²

= 3⁻⁴/3⁻¹⁰ × 1 × t⁻⁶/t⁻¹²

Using the law of exponents,

a^m ÷ aⁿ = a^m-n

= 3^{-4 + 10} × t^{-6 + 12}

= 3⁶ × t⁶

= (3t)⁶

Therefore, the simplified value is (3t)⁶.

✦ Try This: Simplify: (2⁻³)² × (3²)⁻³ × (t⁻²)² / (2⁻²)⁵ × (3³)⁻² × (t⁻²)³

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 180(6)

Simplify: (3⁻²)² × (5²)⁻³ × (t⁻³)² / (3⁻²)⁵ × (5³)⁻² × (t⁻⁴)³

Summary:

The simplified value of (3⁻²)² × (5²)⁻³ × (t⁻³)² / (3⁻²)⁵ × (5³)⁻² × (t⁻⁴)³ is (3t)⁶

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