Answer: Answer choice: [A]: " x⁻ ⁴ " .
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Step-by-step explanation:
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Given:
{x ^ [tex]^( {\frac{-4}{7}) }^7[/tex] ;
→ Simplify.
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Note the following property of exponents:
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→ (xᵃ) ᵇ = x ⁽ ᵃ * ᵇ ⁾ ; {a ≠ 0 ; b ≠ 0 .} .
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As such:
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→ {x ^ [tex]^( {\frac{-4}{7}) }^7[/tex] ;
= x ^ ([tex][(\frac{-4}{7}) * 7 ][/tex] ;
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Find: [tex][(\frac{-4}{7}) * 7 ] ;
Note: " 7 = [tex]\frac{7}{1}[/tex] " .
So: Find: " [tex][(\frac{-4}{7} * [tex]\frac{7}{1}[/tex] " ;
The 2 (two) "7 's " ; cancel out to "1" ;
→ {since: " 7 ÷ 7 = 1 " } ;
And we have:
-4 * 1 = -4 .
So, we have:
" x ⁻ ⁴ " ; which is: Answer choice: [A]: " x⁻ ⁴ " .
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Choice: [C} — is also an equivalent; however, the question asks for the "simplest form" — which is: Answer choice: [A].
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