To solve [tex]\(\left(\sqrt[3]{5^2}\right)^6\)[/tex], we will break it down into smaller steps for clarity.
### Step 1: Calculate [tex]\(5^2\)[/tex]
First, let's find the value of [tex]\(5^2\)[/tex]. This is straightforward:
[tex]\[ 5^2 = 25 \][/tex]
### Step 2: Find the cube root of [tex]\(5^2\)[/tex]
Next, compute the cube root of [tex]\(5^2\)[/tex]. Since [tex]\(5^2 = 25\)[/tex], we need:
[tex]\[ \sqrt[3]{25} \][/tex]
Through calculation, the cube root of 25 is approximately:
[tex]\[ \sqrt[3]{25} \approx 2.924017738212866 \][/tex]
### Step 3: Raise the result to the 6th power
Finally, we take the result from Step 2 and raise it to the 6th power:
[tex]\[ (2.924017738212866)^6 \][/tex]
Performing this calculation yields:
[tex]\[ (2.924017738212866)^6 = 625.0 \][/tex]
### Conclusion
Putting it all together, we find:
[tex]\[ \left(\sqrt[3]{5^2}\right)^6 = 625.0 \][/tex]
