Find the value of x so that (-2)³ × (-2)^-6 = (-2)^{2x - 1}.

Solution:

Given, the expression is (-2)³ × (-2)^-6 = (-2)^{2x - 1}.

We have to find the value of x.

LHS: (-2)³ × (-2)^-6

Using law of exponents,

a^m × aⁿ = a^{m + n}

From the expression (-2)³ × (-2)⁻⁶,

a = -2

m = 3

n = -6

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

= 3 - 6

= -3

a^{m + n} = (-2)⁻³

RHS: (-2)^{2x - 1}

(-2)^{2x - 1} = (-2)⁻³

Now, 2x - 1 = -3

2x = -3 + 1

2x = -2

x = -2/2

x = -1

Therefore, the value of x is -1.

✦ Try This: Find the value of x so that (3)² × (3)⁻⁵ = (3)ˣ⁻³.

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 99(ii)

Find the value of x so that (-2)³ × (-2)^-6 = (-2)^{2x - 1}

Summary:

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

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