Question

4*81 to the power of -1/2(81 to the power 1/2+81 to the power 3/2)

Answer 1

Heya !!!
$4 \times {81}^{ - \frac{1}{2} } ( {81}^{ \frac{1}{2} } + {81}^{ \frac{3}{2} } ) \\ \\ = 4 \times {(9)}^{2 \times - \frac{1}{2} } ( {(9)}^{2 \times \frac{1}{2} } + {(9)}^{2 \times \frac{3}{2} } ) \\ \\ = 4 \times {9}^{ - 1} ( 9 + {9}^{3}) \\ \\ = 4 \times \frac{1}{9} (9 + 729) \\ \\ = \frac{4}{9} \times 738 \\ \\ = 4 \times 82 \\ \\ = 328$

Hope this helps ☺

Answer 2

4 × (81)^-1/2 [(81^1/2+81^3/2)]

= 4 × (9^2)-1/2 [(9^2×1/2+9^2×3/2)]

= 4 × 9^-1× (9^1+9^3)

= 4 × 1/9 × 9 ( 1+ 81)

= 4 × 82

= 328