Question

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

Answer 1

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)`