Question

question
express (left(16^{3}
ight)^{\frac{1}{4}}) in simplest radical form.

Explanation:

Step1: Apply exponent power rule

Using the power - of - a - power rule \((a^{m})^{n}=a^{m\times n}\), for \((16^{3})^{\frac{1}{4}}\), we have \(16^{3\times\frac{1}{4}} = 16^{\frac{3}{4}}\)

Step2: Rewrite 16 as a power of 2

Since \(16 = 2^{4}\), we can substitute \(16\) with \(2^{4}\) in the expression \(16^{\frac{3}{4}}\). So we get \((2^{4})^{\frac{3}{4}}\)

Step3: Apply the power - of - a - power rule again

Using the power - of - a - power rule \((a^{m})^{n}=a^{m\times n}\) for \((2^{4})^{\frac{3}{4}}\), we have \(2^{4\times\frac{3}{4}}=2^{3}\)

Step4: Calculate the value of \(2^{3}\)

We know that \(2^{3}=8\)

Answer:

\(8\)