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Whitepunk [10]
3 years ago
13

.2 to the 5th power

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
7 0

Answer:   The correct answer is:

____________________________________________

        →    " 0.00032 " ; or, write as:  " \frac{1}{3125}  " .

____________________________________________

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) =   \frac{1}{3125} .

___________________________________________

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:

 \frac{1}{3125}  =?  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:  " \frac{1}{3125}  " .

____________________________________________

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