Simplify: 9³ × 27 × t⁴ / (3)⁻² × 3⁴ × t².

Solution:

Given, the expression is 9³ × 27 × t⁴ / (3)⁻² × 3⁴ × t².

We have to simplify the expression.

We know, 9 = 3²

So, 9³ = (3²)³

Using the law of exponents,

(a^m)ⁿ = a^mn

(3²)³ = 3⁶

Also, 27 = 3³

Considering 9³ × 27,

9³ × 27 = 3⁶ × 3³

Using the law of exponents,

a^m × aⁿ = a^{m + n}

= 3^{6 + 3}

= 3⁹

Similarly, (3)⁻² × 3⁴ = 3^{-2 + 4}

= 3²

Now, 9³ × 27 × t⁴ / (3)⁻² × 3⁴ × t² = 3⁹ × t⁴ / 3² × t²

= (3⁹/3²) × (t⁴/t²)

Using the law of exponents,

a^m ÷ aⁿ = a^{m - n}

= 3^{9 - 2} × t^{4 - 2}

= 3⁷ × t²

Therefore, the simplified value is 3⁷ × t².

✦ Try This: Simplify: 2³ × 32 × t⁴ / (2)⁻² × 2⁴ × t².

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 180(5)

Simplify: 9³ × 27 × t⁴ / (3)⁻² × 3⁴ × t²

Summary:

The simplified value of 9³ × 27 × t⁴ / (3)⁻² × 3⁴ × t² is 3⁷ × t² using the law of exponents

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