Find x so that (2/9)³ × (2/9)^-6 = (2/9)^{2x - 1}

Solution:

Given, (2/9)³ × (2/9)^-6 = (2/9)^{2x - 1}

We have to find the value of x.

Considering (2/9)³ × (2/9)⁻⁶,

Using law of exponents,

a^m × aⁿ = a^{m + n}

Here, a = 2/9

m = 3

n = -6

So, m + n = 3 + (-6)

= 3 - 6

= -3

(2/9)³ × (2/9)⁻⁶ = (2/9)⁻³

Now, (2/9)^{2x - 1} = (2/9)⁻³

2x - 1 = -3

2x = -3 + 1

2x = -2

x = -2/2

x = -1

Therefore, the value of x is -1.

✦ Try This: Find x so that (3/5)⁵ × (3/5)⁻⁹ = (3/5)²ˣ

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 116

Find x so that (2/9)³ × (2/9)^-6 = (2/9)^{2x - 1}

Summary:

The value of x so that (2/9)³ × (2/9)^-6 = (2/9)^{2x - 1} is -1 using the law of exponents

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