Question

Simplify:- 4k^2(4^-1k+4k^-2)

Answer 1

Given : 4k^2(4^-1k+4k^-2)    4k²(4⁻¹k  + 4k⁻²)

To find : Simplify

Solution:

4k²(4⁻¹k  + 4k⁻²)

using a (b + c )  = ab  + ac

= 4k². 4⁻¹k   +  4k² . 4k⁻²

Using aⁿ = 1/a⁻ⁿ   or a⁻ⁿ = 1/aⁿ

= 4k² (1/4¹) k    + 4k² . 4/k²

= k².k 4 (1/4) + 4*4 . k²/k²

using xᵃ.xᵇ = x⁽ᵃ⁺ᵇ)

= k⁽²⁺¹)  + 16

= k³ + 16

 4k²(4⁻¹k  + 4k⁻²) = k³ + 16

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