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

Mathematics

2 answers:

makkiz [27]4 years ago

5 0

The answer is: " 5⁻ ⁵⁰ " .
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Note that: |7-9| = <span>| -2 | = 2 .
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Note: 5</span>³ * 5⁻⁵ = 5⁽ ⁽³⁾ ⁺ ⁽⁻⁵⁾ ⁾ = 5⁽³ ⁻ ⁵⁾ = 5⁻² ;
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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⁾
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→ [ 5⁽⁻²⁴⁾ ] ² = 5⁽⁻²⁴ * ²⁾ = 5⁽⁻⁴⁸⁾ ;
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Now, rewrite the entire problem; and solve:

→ 5⁽⁻⁴⁸⁾ * 5⁻² = 5⁽⁻⁴⁸⁾ ⁺ ⁽⁻²⁾ = 5⁽⁻⁴⁸⁻²⁾ ;

= 5⁻ ⁵⁰ .
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