[( 3)^4÷ 3^5]× 3^7 ⇒ ( 1)^4[(3)^4÷ 3^5]× 3^7 #160; #160; #160; [a^b÷ a^c=a^b c] ⇒ ( 1)^4(3)^4 5× 3^7 #160; #160; #160; ...

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Division of a Polynomial by a Polynomial

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Question

Solve
$[(- 3)^{4} \div 3^{5}] \times 3^{7}$

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Solution

$[(- 3)^{4} \div 3^{5}] \times 3^{7}$
$\Rightarrow (- 1)^{4} [(3)^{4} \div 3^{5}] \times 3^{7}$ $[a^{b} \div a^{c} = a^{b - c}]$
$\Rightarrow (- 1)^{4} (3)^{4 - 5} \times 3^{7}$ $[a^{b} \times a^{c} = a^{b + c}]$
$\Rightarrow 1 \times 3^{- 1 + 7} = 3^{6} = 729$ .

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