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

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Answer 1 · 2018-06-01T02:16:54

See a solution process below:

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#