Question

Simplify (144^(-3/2))(-1/6)

Answer 1

Solution :

I think it may be like this ,

[( 144 )^(-3/2 ]^(1/6)

= [ (12)² ]^(-3/2 × 1/6 )

[ Since , (a^m)^n = a^mn ]

=[ ( 12)² ]^-1/4

= ( 12 )^[ 2 ( -1/4 )]

= ( 12 )^-1/2

= 1/(√12 )

= 1/√( 2×2×3)

= 1/2√3

= (√3)/[2√3×√3]

= √3/6

••••

Answer 2

Answer:

$(144^{-\frac{3}{2} })(-\frac{1}{6} ) =-\frac{1}{10368}$

Step-by-step explanation:

$(144^{-\frac{3}{2} })(-\frac{1}{6} )\\=-(\frac{1}{144})^{\frac{3}{2}} (\frac{1}{6})\\=-(\frac{1}{144\sqrt{144} }) (\frac{1}{6})\\=-(\frac{1}{144*12}) (\frac{1}{6})\\=-\frac{1}{10368}$

∴$(144^{-\frac{3}{2} })(-\frac{1}{6} ) =-\frac{1}{10368}$