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] " .
____________________________________________
