How do you evaluate the expression #4^-7/4^-3# using the properties?

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Answer 1 · 2017-05-30T15:32:33

See a solution process below:

We can use this rule of exponents to simplify the expression:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#4^color(red)(-7)/4^color(blue)(-3) => 1/4^(color(blue)(-3)-color(red)(-7)) => 1/4^(color(blue)(-3)+color(red)(7)) => 1/4^4 => 1/256#

Answer 2 · 2017-05-30T15:35:06

#4^-4#

#=1/256#

The problem can be written as #4^(-7-(-3))# because when you divide exponentials, you subtract them.

=#4^(-7+3)#

=#4^-4#

However, the indices should be positive in the answer.

#=1/4^4#

#= 1/256#