How do you simplify #((2c^3d^5)/(5g^2))^5#?

1 Answer
Mar 18, 2017

Answer:

See the entire solution process below:

Explanation:

First, use this rule of exponents to rewrite the constants in the expression: #a = a^color(red)(1)#

#(2^color(red)(1)c^3d^5)/(5^color(red)(1)g^2)#

Next, use this rule of exponents to eliminate the outer exponent:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#((2^color(red)(1)c^color(red)(3)d^color(red)(5))/(5^color(red)(1)g^color(red)(2)))^color(blue)(5) = (2^(color(red)(1) xx color(blue)(5))c^(color(red)(3) xx color(blue)(5))d^(color(red)(5) xx color(blue)(5)))/(5^(color(red)(1) xx color(blue)(5))g^(color(red)(2) xx color(blue)(5))) = (2^5c^15d^25)/(5^5g^10)#

If we expand the constants the result is:

#(32c^15d^25)/(3125g^10)#