Question

How do you simplify the expression `(7c^7d^2)^-2` using the properties?

Answer 1

See the entire simplification process below:

Explanation:

First, use these two rules for exponents to remove the outer exponent from the expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(7c^7d^2)^-2 = (7^color(red)(1)c^color(red)(7)d^color(red)(2))^color(blue)(-2) = 7^(color(red)(1) xx color(blue)(-2))c^(color(red)(7) xx color(blue)(-2))d^(color(red)(2) xx color(blue)(-2)) =`

`7^-2c^-14d^-4`

Now, use this rule for exponents to eliminate the negative exponents:

`x^color(red)(a) = 1/x^color(red)(-a)`

`7^color(red)(-2)c^color(red)(-14)d^color(red)(-4) = 1/(7^color(red)(- -2)c^color(red)(- -14)d^color(red)(- -4)) = 1/(7^2c^14d^4) = 1/(49c^14d^4)`