125 × x⁻³ / 5⁻³ × 25 × x⁻⁶.

Solution:

Given, 125 × x⁻³ / 5⁻³ × 25 × x⁻⁶

We have to find the value of the given expression.

We know, 125 = 5³

25 = 5²

Now, 125 × x⁻³ / 5⁻³ × 25 × x⁻⁶ = 5³ × x⁻³ / 5⁻³ × 5² × x⁻⁶

Considering 5⁻³ × 5²,

Using law of exponents,

a^m × aⁿ = a^{m + n}

5⁻³ × 5² = 5^{-3 + 2} = 5⁻¹

Now, 5³ × x⁻³ / 5⁻³ × 5² × x⁻⁶ = 5³ × x⁻³ / 5⁻¹ × x⁻⁶

= 5³/5⁻¹ × x⁻³/x⁻⁶

Using law of exponents,

a^m ÷ aⁿ = a^{m - n}

= 5^{3 + 1} × x^{-3 + 6}

= 5⁴ × x³

= 625x³

Therefore, the required value is 625x³.

✦ Try This: 625 × x⁻³ / 5⁴ × 125 × x⁻⁶.

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 120

125 × x⁻³ / 5⁻³ × 25 × x⁻⁶

Summary:

125 × x⁻³ / 5⁻³ × 25 × x⁻⁶ = 625x³ using the law of exponents a^m × aⁿ = a^{m + n} and a^m ÷ aⁿ = a^{m - n}

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