What is (5^-9×5^-2 ÷ 5^-13)^ |7-9| × (5^3 × 5^-5) =

The answer is:  "  5⁻ ⁵⁰  " .

Note that:  |7-9| = | -2 |  =  2 .

Note:  5³ * 5⁻⁵ = 5⁽ ⁽³⁾ ⁺ ⁽⁻⁵⁾ ⁾ = 5⁽³ ⁻ ⁵⁾ = 5⁻²  ; 

Note:  (5⁻⁹ * 5⁻² ÷ 5⁻¹³) = (5⁻⁹ * 5⁻²) ÷ 5⁻¹³ ; 

    → (5⁻⁹ * 5⁻²) = 5⁽⁻⁹⁾ ⁺ ⁽⁻²⁾ = 5 ⁽⁻⁹ ⁻ ²⁾ = 5 ⁻¹¹ ;

          →5 ⁻¹¹ ÷ 5⁻¹³  =  5 ⁽⁻¹¹⁾ ⁺ ⁽⁻¹³⁾  = 5⁽⁻¹¹ ⁻ ¹³⁾ = 5⁽⁻²⁴⁾ 

→ [ 5⁽⁻²⁴⁾ ] ²  = 5⁽⁻²⁴ * ²⁾  = 5⁽⁻⁴⁸⁾ ;

  Now, rewrite the entire problem; and solve:
 
 →      5⁽⁻⁴⁸⁾  * 5⁻²  =  5⁽⁻⁴⁸⁾ ⁺ ⁽⁻²⁾  =  5⁽⁻⁴⁸⁻²⁾ ; 

                                                   =  5⁻ ⁵⁰ .

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