Question

1000^(6/4) in radical form

Answer 1

To express \( 1000^{(6/4)} \) in radical form, we first simplify the exponent:

\[
\frac{6}{4} = \frac{3}{2}
\]

So, we have:

\[
1000^{(6/4)} = 1000^{(3/2)}
\]

Now, we can express \( 1000^{(3/2)} \) in radical form:

\[
1000^{(3/2)} = (1000^{3})^{\frac{1}{2}} = \sqrt{1000^{3}}
\]

Next, we simplify \( 1000^{3} \):

\[
1000 = 10^3 \quad \text{so} \quad 1000^{3} = (10^3)^{3} = 10^{9}
\]

Thus, we can rewrite \( \sqrt{1000^{3}} \):

\[
\sqrt{1000^{3}} = \sqrt{10^{9}} = 10^{\frac{9}{2}} = 10^{4.5} = 10^4 \cdot 10^{0.5} = 10000 \cdot \sqrt{10}
\]

So, the expression \( 1000^{(6/4)} \) in radical form is:

\[
10000\sqrt{10}
\]