Mathematics, 15.07.2019 10:00 bunnles

What is 7 over (fraction bar) (8×4)+90÷9 ÷ (6^3)^-2 × 9 over (fraction bar) 6(5+4) =

$What is 7 over (fraction bar) (8×4)+90÷9 ÷ (6^3)^-2 × 9 over (fraction bar) 6(5+4) =$

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Answer from: kernlife

The answer is: " 36 " .
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Note: " (8 * 4) + 90 ÷ 9 " =  " (8 * 4) + (90 ÷ 9) " = "32 + 10 = 42" .

We can rewrite the "fraction":

7 / [ (8 * 4) + 90 ÷ 9 ] ; as: $\frac{7}{42}$ ;

and can reduce this value to (and rewrite as): " $\frac{1}{6}$ " ;
{ since: " $\frac{7}{42}$ = $\frac{7/7}{42/7}$ = $\frac{1}{6}$ " .}.

Note: The "fraction" : $\frac{9}{6(5+4)}$ ; the "9/6" cancel to "3/2" ;
{Since: "9÷3 = 3" ; and since: "6÷3 = 2" ).

So rewrite: $\frac{9}{6(5+4)}$ ; as:

$\frac{3}{2(5+4)}$ ;

Note: $\frac{3}{2(5+4)}$ ;

= $\frac{3}{2(9)}$ ;

= $\frac{3}{18}$ ;

→ Note:    $\frac{3}{18}$ ; can be reduced to; & rewritten as:

" $\frac{1}{6}$ " ;

→ {since: " $\frac{3}{18}$ =   $\frac{3/3}{18/3}$ ;

=    $\frac{1}{6}$ ;
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Note that: (6²) ⁻² = 6⁽ ² * ⁻²⁾ = 6⁻ ⁴ ;

= $\frac{1}{6^4}$ ;
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So, we can rewrite our expression as:

$\frac{1}{6}$ ÷ $\frac{1}{6^4}$ * $\frac{1}{6}$ ;
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Note:
_________________________________________________________
$\frac{1}{6}$ ÷ $\frac{1}{6^4}$ * $\frac{1}{6}$ ;

= ( $\frac{1}{6}$ ÷ $\frac{1}{6^4}$ ) * $\frac{1}{6}$ ;

= ( $\frac{1}{6}$ * $\frac{6^4}{1}$ ) * $\frac{1}{6}$ ;

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Start with :
________________________________________________________
→ ( $\frac{1}{6}$ * $\frac{6^4}{1}$ ) ;

The "6" in the " $\frac{1}{6}$ " ; cancels to a "1" ;
and the "6⁴ " in the " $\frac{6^4}{1}$ ) " ; cancels to a "6³ " ;

→ {Since: "6⁴ / 6 = 6⁴ / 6¹ = 6⁽⁴ ⁻ ¹⁾ = 6³ ;

→ and we have:    $\frac{1}{1}$ * $\frac{6^3}{1}$ ;

→ The " $\frac{1}{1}$ " can be eliminated; since "1÷1= 1 " ;
and since: any value, divided by "1", equal that same value; & since "any value, multiplied by "1"; equals that same value" ;
________________________________________________________
We have: " 6³ " .
________________________________________________________

Now, we multiplied this value, " 6³ " , by " $\frac{1}{6}$ " ;

→ 6³ * $\frac{1}{6}$ ;

= $\frac{6^3}{1}$ * $\frac{1}{6}$ ;

Note: The "6³ " cancels out to "6² " ; and the "6" cancels out to "1" ;

{since: "6³ ÷ 6 = 6³ ÷ 6¹ = 6⁽³ ⁻ ¹⁾ = 6² " ;
and since: "6 ÷ 6 = 1 " ; ________________________________________________________
→ The answer is: 6² = 6 * 6 = 36 ;
________________________________________________________
The answer is: " 36 " .
________________________________________________________

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