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In the given question we have to simplify each expression:

$鈸�c^{鈭�8}路c^{鈭�7}鈸�(r^5{s}^{鈭�3})\left(r^{鈭�7}{s}^{鈭�5}\right)鈸�(-6c^{鈭�6}{d}^4)(鈭�5c^{-2}{d}^{鈭�1})$

Add the exponents, since the bases are the same.

$c^{鈭�8}路c^{鈭�7}=c^{鈭�8鈭�7}$

Simplify.

$c^{鈭�8}路c^{鈭�7}=c^{鈭�15}$

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

$c^{鈭�8}路c^{鈭�7}=\frac{1}{c^{15}}$

Use the Commutative Property to get like bases together.

Add the exponents, since the bases are the same.

$(r^5{s}^{鈭�3})\left(r^{鈭�7}{s}^{鈭�5}\right)=\left(r^{5鈭�7}\right)\left(s^{鈭�3鈭�5}\right)$

Simplify.

$(r^5{s}^{鈭�3})\left(r^{鈭�7}{s}^{鈭�5}\right)=\left(r^{鈭�2}\right)\left(s^{鈭�8}\right)$

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

$(r^5{s}^{鈭�3})\left(r^{鈭�7}{s}^{鈭�5}\right)=\left(\frac{1}{r^2}\right)\left(\frac{1}{s^8}\right)$

$(r^5{s}^{鈭�3})\left(r^{鈭�7}{s}^{鈭�5}\right)=\frac{1}{r^2{s}^8}$

Use the Commutative Property to get like bases together.

$(-6c^{鈭�6}{d}^4)(鈭�5c^{-2}{d}^{鈭�1})=(-6)路(鈭�5)\left(c^{鈭�6}{c}^{-2}\right)\left(d^{鈭�1}{d}^4\right)$

Add the exponents, since the bases are the same.

$(-6c^{鈭�6}{d}^4)(鈭�5c^{-2}{d}^{鈭�1})=(-6)路(鈭�5)\left(c^{鈭�6-2}\right)\left(d^{鈭�1+4}\right)$

Simplify.

$(-6c^{鈭�6}{d}^4)(鈭�5c^{-2}{d}^{鈭�1})=30\left(c^{鈭�8}\right)\left(d^3\right)$

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

$(-6c^{鈭�6}{d}^4)(鈭�5c^{-2}{d}^{鈭�1})=30\left(\frac{1}{c^8}\right)\left(d^3\right)$

$(-6c^{鈭�6}{d}^4)(鈭�5c^{-2}{d}^{鈭�1})=\frac{30d^3}{c^8}$