(-1/7)⁻⁵ ÷ (-1/7)⁻⁷ = (-7)ˣ. Find x.

Solution:

Given, the expression is (-1/7)⁻⁵ ÷ (-1/7)⁻⁷ = (-7)ˣ.

We have to find the value of x.

Considering (-1/7)⁻⁵ ÷ (-1/7)⁻⁷,

Using the law of exponents,

a^m ÷ aⁿ = a^{m - n}

(-1/7)⁻⁵ ÷ (-1/7)⁻⁷ = (-1/7)^{-5 + 7}

= (-1/7)²

= -1/7²

Using the law of exponents,

a⁻ⁿ = 1/aⁿ

= (-7)⁻²

Now, (-7)⁻² = (-7)ˣ

On comparing the powers,

x = -2

Therefore, the value of x is -2.

✦ Try This: (-1/5)⁻⁵ ÷ (-1/5)⁻⁶ = (-5)ˣ. Find x.

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

NCERT Exemplar Class 8 Maths Chapter 8 Problem 177(1)

(-1/7)⁻⁵ ÷ (-1/7)⁻⁷ = (-7)ˣ. Find x.

Summary:

(-1/7)⁻⁵ ÷ (-1/7)⁻⁷ = (-7)ˣ. The value of x is -2 using the laws of exponents a^m ÷ aⁿ = a^m-n and a⁻ⁿ = 1/aⁿ

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