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

1 Answer
Mar 19, 2017

Answer:

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)#