.2 to the 5th power

Answer:   The correct answer is:____________________________________________         →    " 0.00032 " ; or, write as:  " [tex]\frac{1}{3125}[/tex]  " .____________________________________________Step-by-step explanation:_______________________________________Method 1) ____________________________________________ (0.2)⁵ = ? ; Note:  " 0.2 " = 2/10  = (2÷2) / (10÷2) = 1/5 .→ (0.2)⁵ = (1/5)⁵ = (1⁵) / (5)⁵ = ? ; Note:  1⁵ = 1 × 1 × 1 × 1× 1 = 1 ;  Note:  5⁵ = 5 × 5 × 5 × 5 × 5 ;                = (5 × 5) × 5 × 5 × 5 ;                =  (25) × 5 × 5 × 5 ;                =  (25 × 5) × 5 × 5 ;                =  125 × 5 × 5 ;                =  (125 × 5)  * 5 ;                =  (625 ) × 5 ;                =   3125 .___________________________________________  →  (0.2)⁵  =  (1/5)⁵ = (1⁵ / 5⁵) =   [tex]\frac{1}{3125}[/tex] .___________________________________________Method 2)____________________________________________(0.2)⁵ = 0.2 ×  0.2 × 0.2 × 0.2 × 0.2 ;           =  (0.2 × 0.2) × 0.2 × 0.2 × 0.2 ;           = (0.04)  ×  (0.2)  × (0.2) × (0.2) ;           =  (0.04 * 0.2)  × 0.2 × 0.2 ;          =  (0.008)  ×  0.2 × 0.2 ;           =  (0.008)  ×  (0.2 × 0.2) ;           =  (0.008)  × (0.04) ; (0.2)⁵ =  0.00032   ____________________________________________Now, just for curiosity, let us see if the values obtained using       both "Method 1" and "Method 2" are equal:  [tex]\frac{1}{3125}[/tex]  =?  0.00032  ?? ;      →   (1 ÷ 3125)  =?  0.00032 ?? ; Yes!____________________________________________Also, check work using calculator:____________________________________________  (0.2)⁵  = 0.00032 .  Yes!____________________________________________The correct answer is:____________________________________________   " 0.00032 " ; or, write as:  " [tex]\frac{1}{3125}[/tex]  " .____________________________________________