Sure! Let's break down the given expression [tex]\(\sqrt[3]{9} \cdot \sqrt{9^7}\)[/tex] step by step:
1. First, let's find the cube root of 9, denoted as [tex]\(\sqrt[3]{9}\)[/tex]. This value is approximately [tex]\(2.080083823051904\)[/tex].
2. Next, we need to calculate [tex]\(9^7\)[/tex]. This operation raises 9 to the power of 7 and evaluates to [tex]\(4782969\)[/tex].
3. Then, we must take the square root of [tex]\(9^7\)[/tex], which is [tex]\(\sqrt{4782969}\)[/tex]. This value is equal to [tex]\(2187.0\)[/tex].
4. Finally, we multiply the cube root of 9 by the square root of [tex]\(9^7\)[/tex]:
[tex]\[
\sqrt[3]{9} \cdot \sqrt{9^7} \approx 2.080083823051904 \times 2187.0
\][/tex]
This multiplication yields the result [tex]\(4549.143321014514\)[/tex].
So, the value of [tex]\(\sqrt[3]{9} \cdot \sqrt{9^7}\)[/tex] is approximately [tex]\(4549.143321014514\)[/tex].
