Sure, I'll help you understand the step-by-step solution for the given expression [tex]\(\left(16^{\frac{1}{2}}\right)^{-6}\)[/tex].
1. Understand the Expression:
- The expression you need to evaluate is [tex]\(\left(16^{\frac{1}{2}}\right)^{-6}\)[/tex].
- This expression involves two operations: finding the square root and raising to a negative power.
2. Calculate the Square Root:
- First, simplify [tex]\(16^{\frac{1}{2}}\)[/tex]. The notation [tex]\(16^{\frac{1}{2}}\)[/tex] represents the square root of 16.
- [tex]\(\sqrt{16} = 4\)[/tex].
3. Raise the Result to the Power of -6:
- Now take the result from the first step, which is 4, and raise it to the power of -6.
- [tex]\(4^{-6}\)[/tex].
4. Simplify the Expression:
- [tex]\(4^{-6}\)[/tex] means [tex]\(\frac{1}{4^6}\)[/tex].
- Calculate [tex]\(4^6\)[/tex]:
- [tex]\(4^2 = 16\)[/tex]
- [tex]\(4^4 = 16^2 = 256\)[/tex]
- [tex]\(4^6 = 256 \times 16 = 4096\)[/tex]
So, [tex]\(4^6 = 4096\)[/tex].
5. Combining Results:
- Therefore, [tex]\(\frac{1}{4^6} = \frac{1}{4096}\)[/tex].
6. Final Answer:
- The result [tex]\(\left(16^{\frac{1}{2}}\right)^{-6}\)[/tex] evaluates to [tex]\(0.000244140625\)[/tex].
Thus, [tex]\(\left(16^{\frac{1}{2}}\right)^{-6} = 0.000244140625\)[/tex].
