Question

125^-5 x 25^-4 x 5^12 Simplyfy

Answer 1

Step-by-step explanation:

Simplify 125−5· 25−4· 512:

1

48828125 (Decimal: 2.048E−8)

Answer 2

125⁻⁵ x 25⁻⁴ x 5¹²  = 5⁻¹¹

Given:

125⁻⁵ x 25⁻⁴ x 5¹²

To Find:

Simplify  125⁻⁵ x 25⁻⁴ x 5¹²

Solution:

Given sum 125⁻⁵ x 25⁻⁴ x 5¹²  

Here 125 = 5 × 5 × 5

          25 = 5 × 5

Now given sum can be written as

⇒ (5³)⁻⁵ x (5²)⁻⁴ x 5¹²  

⇒ 5⁻¹⁵ × 5⁻⁸ × 5¹²             [  ∵ (aⁿ)ˣ  = aⁿˣ ]          

⇒ 5⁻¹⁵⁻⁸⁺¹²                       [ ∵ aᵃ × aᵇ  = aᵃ⁺ᵇ ]    

Here,   - 15 - 8 + 12 = -11

⇒ 5⁻¹⁵⁻⁸⁺¹² = 5⁻¹¹

Therefore,  125⁻⁵ x 25⁻⁴ x 5¹²  = 5⁻¹¹

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