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.

$=1/4^4$

$= 1/256$

How do you evaluate the expression 4^-7/4^-34^-7/4^-3 using the properties?