Question

question
simplify \\(\sqrt{64x^{14}}\\) completely given \\(x > 0\\).

answer attempt 1 out of 5

Explanation:

Step1: Simplify the square root of 64

The square root of 64 is a perfect square, so $\sqrt{64} = 8$ because $8 \times 8 = 64$.

Step2: Simplify the square root of \(x^{14}\)

Using the property of exponents for square roots, $\sqrt{x^{n}} = x^{\frac{n}{2}}$ when $x > 0$. For $n = 14$, we have $\sqrt{x^{14}} = x^{\frac{14}{2}} = x^{7}$.

Step3: Combine the results

Multiply the results from Step 1 and Step 2 together. So $\sqrt{64x^{14}} = \sqrt{64} \times \sqrt{x^{14}} = 8 \times x^{7} = 8x^{7}$.

Answer:

\(8x^{7}\)