How do you simplify #((c^2d^2 )/ (cd^3)) * (d^2 / c^2)^3# leaving only positive exponents?

1 Answer
Mar 15, 2018

Answer:

#((c^2d^2)/(cd^3))*((d^2)/(c^2))^3=color(blue)(d^5/c^5#

Explanation:

Simplify.

#((c^2d^2)/(cd^3))*((d^2)/(c^2))^3#

Apply power rule of exponents: #(a^m)^n=a^(m*n)#

#((c^2d^2)/(cd^3))*(d^((2*3))/(c^((2*3))))#

Simplify.

#((c^2d^2)/(cd^3))*((d^6)/(c^6))#

Remove parentheses.

#(c^2d^2)/(cd^3)*(d^6)/(c^6)#

Apply product rule of exponents: #a^ma^n=a^(m+n)#

No exponent is understood to be an exponent of #1#.

#(c^2d^((2+6)))/(c^((1+6))d^3)#

Simplify.

#(c^2d^8)/(c^7d^3)#

Apply quotient rule of exponents: #(a^m)/(a^n)=a^(m-n)#

#c^((2-7))d^((8-3))#

Simplify.

#c^(-5)d^5#

Apply negative exponent rule: #a^(-m)=1/a^m#

#d^5/c^5#