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In the given question we have to simplify each expression:

$鈸�z^{鈭�4}路z^{鈭�5}鈸�(p^6{q}^{鈭�2})\left(p^{鈭�9}{q}^{鈭�1}\right)鈸�\left(3u^{鈭�5}{v}^7\right)(鈭�4u^4{v}^{鈭�2})$

Add the exponents, since the bases are the same.

$z^{鈭�4}路z^{鈭�5}=z^{鈭�4鈭�5}$

Simplify.

$z^{鈭�4}路z^{鈭�5}=z^{鈭�9}$

Use the definition of a negative exponent i.e.role="math" localid="1644763107906" $a^{-n}=\frac{1}{a^n}$

$z^{鈭�4}路z^{鈭�5}=\frac{1}{z^9}$

Use the Commutative Property to get like bases together.

$(p^6{q}^{鈭�2})\left(p^{鈭�9}{q}^{鈭�1}\right)=(p^6{p}^{鈭�9})路\left(q^{鈭�2}{q}^{鈭�1}\right)$

Add the exponents, since the bases are the same.

$(p^6{q}^{鈭�2})\left(p^{鈭�9}{q}^{鈭�1}\right)=p^{6-9}路q^{鈭�2鈭�1}$

Simplify.

$(p^6{q}^{鈭�2})\left(p^{鈭�9}{q}^{鈭�1}\right)=p^{-3}路q^{鈭�3}$

Use the definition of a negative exponent, i.e. $a^{-n}=\frac{1}{a^n}$

$(p^6{q}^{鈭�2})\left(p^{鈭�9}{q}^{鈭�1}\right)=\frac{1}{p^3路q^3}$

Use the Commutative Property to get like bases together.

$\left(3u^{鈭�5}{v}^7\right)(鈭�4u^4{v}^{鈭�2})=3路(-4)路\left(u^{鈭�5}{u}^4\right)\left(v^7{v}^{鈭�2}\right)$

Add the exponents, since the bases are the same.

$\left(3u^{鈭�5}{v}^7\right)(鈭�4u^4{v}^{鈭�2})=3路(-4)路\left(u^{鈭�5+4}\right)\left(v^{7-2}\right)$

Simplify.

$\left(3u^{鈭�5}{v}^7\right)(鈭�4u^4{v}^{鈭�2})=-12路\left(u^{鈭�1}\right)\left(v^5\right)$

Use the definition of a negative exponent i.e.$a^{-n}=\frac{1}{a^n}$

$\left(3u^{鈭�5}{v}^7\right)(鈭�4u^4{v}^{鈭�2})=-12路\left(\frac{1}{u}\right)\left(v^5\right)$

$\left(3u^{鈭�5}{v}^7\right)(鈭�4u^4{v}^{鈭�2})=\frac{-12v^5}{u}$