Question

.2 to the 5th power

Answer 1

Answer: The correct answer is:

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→ " 0.00032 " ; or, write as: "
`(1)/(3125)` " .

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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) =
`(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:

`(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: "
`(1)/(3125)` " .

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