Respuesta :
Answer: " 4 ,096 horses " .
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Step-by-step 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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Hey there!
[tex]\bold{(4^2)^3\times4^0}[/tex]
- [tex]\bold{4^2=16}[/tex]
- [tex]\bold{(16^3)\times(4^0)}[/tex]
- [tex]\bold{16^3=4,096}[/tex]
- [tex]\bold{4,096\times4^0}[/tex]
- [tex]\bold{4^0=1}[/tex] (whenever you get a number raised to the power of 0, your answer/result will automatically be [tex]\bold{1}[/tex])
- [tex]\bold{4,096\times1=4,096}[/tex]
- [tex]\boxed{\boxed{\bold{Answer:4,096horses}}}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]\bold{LoveYourselfFirst:)}[/tex]
