Question

What is the value of the exponential expression `16^(-3/4)`?

Answer 1

See a solution process below:

Explanation:

First, it is known that: `16 = 2^4`

Therefore, we can rewrite the expression as:

`16^(-3/4) => (2^4)^(-3/4)`

Next, we can use this rule for exponents to eliminate the outer exponent:

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

`(2^color(red)(4))^color(blue)(-3/4) => 2^(color(red)(4) xx color(blue)(-34)) => 2^(-12/4) => 2^-3`

Now we can use this rule for exponents to complete the evaluation:

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

`2^color(red)(-3) => 1/2^color(red)(- -3) => 1/2^color(red)(3) = 1/8`