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

Jun 1, 2018

See a solution process below:

Explanation:

First, it is known that: $16 = {2}^{4}$

Therefore, we can rewrite the expression as:

${16}^{- \frac{3}{4}} \implies {\left({2}^{4}\right)}^{- \frac{3}{4}}$

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

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({2}^{\textcolor{red}{4}}\right)}^{\textcolor{b l u e}{- \frac{3}{4}}} \implies {2}^{\textcolor{red}{4} \times \textcolor{b l u e}{- 34}} \implies {2}^{- \frac{12}{4}} \implies {2}^{-} 3$

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

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${2}^{\textcolor{red}{- 3}} \implies \frac{1}{2} ^ \textcolor{red}{- - 3} \implies \frac{1}{2} ^ \textcolor{red}{3} = \frac{1}{8}$