Question

There are (4^2)^3 ⋅ 4^0 horses on a stud farm. What is the total number of horses on the farm?

Answer 1

Hey there!

`\bold{(4^2)^3*4^0}`

• 
  `\bold{4^2=16}`
• 
  `\bold{(16^3)*(4^0)}`
• 
  `\bold{16^3=4,096}`
• 
  `\bold{4,096*4^0}`
• 
  `\bold{4^0=1}` (whenever you get a number raised to the power of 0, your answer/result will automatically be
  `\bold{1}`)
• 
  `\bold{4,096*1=4,096}`
• 
  `\boxed{\boxed{\bold{Answer:4,096horses}}}`

Good luck on your assignment and enjoy your day!

~
`\bold{LoveYourselfFirst:)}`

Answer 2

Answer: " 4 ,096 horses " .

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Explanation:

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→ " (4 ²) ³ * 4⁰ = ? " ;

Note: " 4⁰ = 1 " ;

{Note the "zero exponent" property: " a⁰ = 1 " ; for: " a ≠ 0 " .}.

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So; we can rewrite our problem as:

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→ " (4 ² ) ³ * 1 = ? " ;

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Note that "any value" ; multiplied by: " 1 " ; results in "that same value" ;

→ so; we can eliminate the: " 1 " ; and rewrite our problem as:

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→ " (4 ² ) ³ " .

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To simplify: " (4² ) ³ = 4 ⁽ ² * ³ ⁾ " ;

{Note the following property of integer exponents} :

→ " (x ᵃ) ᵇ = x ⁽ ᵃ ᵇ ⁾ " . } .

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→ " 4 ⁽ ² * ³ ⁾ = 4 ⁶ " ;

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→ " 4 ⁶ = 4,096 " . ← {Use calculator.}.

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→ Or;

→ " 4 ⁶ " = " 4 * 4 * 4 * 4 * 4 * 4 " ;

= " (4 * 4) * (4 * 4) * (4 * 4) " ;

= " (16) * (16) * (16) " ;

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Note the following calculations:

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₃

16

* 16

_______

₁ 9 6

⁺ 1 6

2 5 6 ;

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₃ ₃

→ 2 5 6

* 1 6 __

¹

1 5 3 6

⁺ 2 5 6

4 0 9 6 .

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→ The answer is: " 4, 096 horses " .

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Or:

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" 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 = ? " ;

→ " 4 * 4 * 4 * 4 * 4 * 4 ;

= (4 * 4) * 4 * 4 * 4 * 4 ;

= 16 * 4 * 4 * 4 * 4 ;

= (16 * 4) * 4 * 4 * 4 ;

= (64) * 4 * 4 * 4 ;

= (64 * 4) * 4 * 4 ;

= (256) * 4 * 4 ;

= (256 * 4) * 4 ;

= (1,024) * 4 ;

= 1,024 * 4 ;

= " 4 ,096 " .

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The answer is: " 4 ,096 horses " .

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Alternate approach:

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" (4 ² )³ = ? " ;

→ Take the value in parentheses: " (4² = 4 * 4 = 16 ) " ;

→ Rewrite as: " 16³ = ? " ; and solve using calculator;

{or; "by hand" ; such as done above}:

→ Or: " 16³ = 16 * 16 * 16 = ? " ;

= (16 * 16) * 16 ;

= (256) * 16 ;

= 256 * 16 ;

= " 4,096 " .

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→ " 16³ = 16 * 16 * 16 = 4,096 " .

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The answer is: " 4, 096 horses " .

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Hope this helps you!

Wishing you the best!

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