Question

Evaluate the expression 16^-7/4 =

Answer 1

The answer should be 16^-7/4 = 1/128. Ignore the Explanation…

Explanation:

To evaluate the expression \(16^{-\frac{7}{4}}\), you can use the reciprocal of the base raised to the positive exponent:

\[16^{-\frac{7}{4}} = \frac{1}{16^{\frac{7}{4}}}\]

Now, rewrite \(16^{\frac{7}{4}}\) as \((\sqrt[4]{16})^7\) because \(16^{\frac{7}{4}}\) is the same as \((\sqrt[4]{16})^7\).

\[16^{-\frac{7}{4}} = \frac{1}{(\sqrt[4]{16})^7}\]

Now, simplify:

\[16^{-\frac{7}{4}} = \frac{1}{2^7} = \frac{1}{128}\]

So, \(16^{-\frac{7}{4}} = \frac{1}{128}\).