Find the value of n so that 6ⁿ/6⁻² = 6³

Solution:

Given, 6ⁿ/6⁻² = 6³

We have to find the value of n.

Considering 6ⁿ/6⁻²,

Using law of exponents,

a⁻ⁿ = 1/aⁿ

6⁻² = 1/6⁻² = 6²

So, 6ⁿ/6⁻² = 6ⁿ × 6²

Using law of exponents,

a^m × aⁿ = a^{m + n}

So, 6ⁿ × 6² = 6^{n + 2}

Now, 6^{n + 2} = 6³

n + 2 = 3

n = 3 - 2

n = 1

Therefore, the value of n is 1.

✦ Try This: Find the value of n so that 8ⁿ/8⁻² = 8⁴

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 118

Find the value of n so that 6ⁿ/6⁻² = 6³

Summary:

The value of n so that 6ⁿ/6⁻² = 6³ is 1 using the law of exponents a⁻ⁿ = 1/aⁿ

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