Question

.2 to the 5th power

Answer 1

Answer:   The correct answer is:

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

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Step-by-step explanation:

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Method 1)

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(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 .

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→  (0.2)⁵  =  (1/5)⁵ = (1⁵ / 5⁵) =   $\frac{1}{3125}$ .

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Method 2)

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(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  

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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!

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Also, check work using calculator:

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 (0.2)⁵  = 0.00032 .  Yes!

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The correct answer is:

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

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