Question

Simplify. Assume all variables are positive.
(16t)^( 3/4 )

Answer 1

To simplify \((16t)^{3/4}\), we can apply the properties of exponents.

First, we can separate the expression into two parts:

\[
(16t)^{3/4} = 16^{3/4} \cdot t^{3/4}
\]

Now, let's simplify \(16^{3/4}\):

1. Since \(16\) can be rewritten as \(2^4\):

\[
16^{3/4} = (2^4)^{3/4}
\]

2. We can use the property of exponents \((a^m)^n = a^{m \cdot n}\):

\[
(2^4)^{3/4} = 2^{4 \cdot (3/4)} = 2^3
\]

3. Now, calculate \(2^3\):

\[
2^3 = 8
\]

Now, we can combine this with \(t^{3/4}\):

\[
(16t)^{3/4} = 8 \cdot t^{3/4}
\]

Thus, the final simplified form is:

\[
\boxed{8t^{3/4}}
\]